Goswami Publications

SCIENTIFIC PUBLICATIONS

Ambarish Goswami

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International Journals

Gabriel Aguirre-Ollinger, J. Edward Colgate, Michael A. Peshkin, and A. Goswami,
Design of an Active 1-DOF Lower-Limb Exoskeleton with Inertia Compensation,
The International Journal of Robotics Research, Month, Year (accepted).
(pdf).

Abstract
Limited research has been done on exoskeletons to enable faster movements of the lower extremities. An exoskeleton's mechanism can actually hinder agility by adding weight, inertia and friction to the legs; compensating inertia through control is particularly dicult due to instability issues. The added inertia will reduce the natural frequency of the legs, probably leading to lower step frequency during walking. We present a control method that produces an approximate compensation of an exoskeleton's inertia. The aim is making the natural frequency of the exoskeleton-assisted leg larger than that of the unaided leg. The method uses admittance control to compensate the weight and friction of the exoskeleton. Inertia compensation is emulated by adding a feedback loop consisting of low-pass ltered acceleration multiplied by a negative gain. This gain simulates negative inertia in the low-frequency range. We tested the controller on a statically supported, single-DOF exoskeleton that assists swing movements of the leg. Subjects performed movement sequences, rst unassisted and then using the exoskeleton, in the context of a computer-based task resembling a race. With zero inertia compensation, the steady-state frequency of leg swing was consistently reduced. Adding inertia compensation enabled subjects to recover their normal frequency of swing.

Gabriel Aguirre-Ollinger, J. Edward Colgate, Michael A. Peshkin, and A. Goswami,
A 1-DOF Assistive Exoskeleton with Inertia Compensation: Effects on the Agility of Leg Swing Motion,
Proceedings of the Institution of Mechanical Engineers, Part H, Journal of Engineering in Medicine, Month, Year (accepted).
(pdf).

Abstract
Many of the current implementations of exoskeletons for the lower extremities are conceived to either augment the user’s load-carrying capabilities or reduce muscle activation during walking. Comparatively little research has been conducted on enabling an exoskeleton to increase the agility of lower-limb movements. One obstacle in this regard is the inertia of the exoskeleton’s mechanism, which tends to reduce the natural frequency of the human limbs. A control method is presented that produces an approximate compensation of the inertia of an exoskeleton’s mechanism. The controller was tested on a statically mounted, single- DOF exoskeleton that assists knee flexion and extension. Test subjects performed multiple series of leg-swing movements in the context of a computer-based, sprint-like task. A large initial acceleration of the leg was needed for the subjects to track a virtual target on a computer screen. The uncompensated inertia of the exoskeleton mechanism slowed down the transient response of the subjects’ limb, in comparison with trials performed without the exoskeleton. The subsequent use of emulated inertia compensation on the exoskeleton allowed the subjects to improve their transient response for the same task.

R. C. Browning, J. R. Modica, R. Kram and A. Goswami,
The effects of adding mass to the legs on the enrgetics and biomechanics of walking,
Medicine and Science in Sports and Exercise, March, 2007.
(pdf).

Purpose:
The metabolic cost of walking increases when mass is added to the legs, but the effects of load magnitude and location on the energetics and biomechanics of walking are unclear. We hypothesized that with leg loading 1) net metabolic rate would be related to the moment of inertia of the leg (I_leg), 2) kinematics would be conserved, except for heavy foot loads, and 3) swing-phase sagittal-plane net muscle moments and swing-phase leg-muscle electromyography (EMG) would increase. Methods: Five adult males walked on a forcemeasuring treadmill at 1.25 ms^-1 with no load and with loads of 2 and 4 kg per foot and shank, 4 and 8 kg per thigh, and 4, 8, and 16 kg on the waist. We recorded metabolic rate and sagittal-plane kinematics and net muscle moments about the hip, knee, and ankle during the single-stance and swing phases, and EMG of key leg muscles. Results: Net metabolic rate during walking increased with load mass and more distal location and was correlated with Ileg (r^2 = 0.43). Thigh loading was relatively inexpensive, helping to explain why the metabolic rate during walking is not strongly affected by body mass distribution. Kinematics, single-stance and swing-phase muscle moments, and EMG were similar while walking with no load or with waist, thigh, or shank loads. The increase in net metabolic rate with foot loading was associated with greater EMG of muscles that initiate leg swing and greater swing-phase muscle moments. Conclusions: Distal leg loads increase the metabolic rate required for swinging the leg. The increase in metabolic rate with more proximal loads may be attributable to a combination of supporting (via hip abduction muscles) and propagating the swing leg.

M. B. Popovic, A. Goswami, and H. Herr,
Ground reference points in legged locomotion: Definitions, biological trajectories and control implications,
International Journal of Robotics Research, Vol. 24, No. 12, 2005.
(pdf).

Abstract:
The zero moment point (ZMP), foot rotation indicator (FRI) and centroidal moment pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. In this paper, we study these reference points for normal human walking, and discuss their applicability in legged machine control. Since the FRI was proposed as an indicator of foot rotation, we hypothesize that the FRI will closely track the ZMP in early single support when the foot remains flat on the ground, but will then significantly diverge from the ZMP in late single support as the foot rolls during heel-off. Additionally, since spin angular momentum has been shown to remain small throughout the walking cycle, we hypothesize that the CMP will never leave the ground support base throughout the entire gait cycle, closely tracking the ZMP. We test these hypotheses using a morphologically realistic human model and kinetic and kinematic gait data measured from ten human subjects walking at self-selected speeds. We find that the mean separation distance between the FRI and ZMP during heel-off is within the accuracy of their measurement (0.1% of foot length). Thus, the FRI point is determined not to be an adequate measure of foot rotational acceleration and a modified FRI point is proposed. Finally, we find that the CMP never leaves the ground support base, and the mean separation distance between the CMP and ZMP is small (14% of foot length), highlighting how closely the human body regulates spin angular momentum in level ground walking.

S. Goldenstein, M. Karavelas, D. Metaxas, L. Guibas, E. Aaron, and A. Goswami,
Scalable nonlinear dynamical systems for agent steering and crowd simulation,
Computers and Graphics, Vol. 25, No. 6, 2001.
(pdf).

Abstract:
We present a new methodology for agent modeling that is scalable and efficient. It is based on the integration of nonlinear dynamical systems and kinetic data structures. The method consists of three-layers, which together model 3D agent steering, crowds and flocks among moving and static obstacles. The first layer, the local layer employs nonlinear dynamical systems theory to models low-level behaviors. It is fast and efficient, and it does not depend on the total number of agents in the environment. This dynamical systems-based approach also allows us to establish continuous numerical parameters for modifying each agent’s behavior. The second layer, a global environment layer consists of a specifically designed kinetic data structure to track efficiently the immediate environment of each agent and know which obstacles/agents are near or visible to the given agent. This layer reduces the complexity in the local layer. In the third layer, a global planning layer, the problem of target tracking is generalized in a way that allows navigation in maze-like terrains, avoidance of local minima and cooperation between agents. We implement this layer based on two approaches that are suitable for different applications: One approach is to track the closest single moving or static target; the second is to use a pre-specified vector field, which may be generated automatically (with harmonic functions, for example) or based on user input to achieve tht desired output. We also discuss how hybrid systems concepts for global planning can capitalize on both our layered approach and the continuous, reactive nature of our agent steering.

We demonstrate the power of the approach through a series of experiments simulating single/multiple agents and crowds moving towards moving/static targets in complex environments.

D. Tolani, A. Goswami, and N. I. Badler
Real-time inverse kinematics techniques for anthropomorphic limbs,
Graphical Models, Vol. 62, No. 5, 2000.
(pdf).

Abstract:
In this paper we develop a set of inverse kinematics algorithms suitable for an anthropomorphic arm or leg. We use a combination of analytical and numerical methods to solve generalized inverse kinematics problems including position, orientation, and aiming constraints. Our combination of analytical and numerical methods results in faster and more reliable algorithms than conventional inverse Jacobian and optimization-based techniques. Additionally, unlike conventional numerical algorithms, our methods allow the user to interactively explore all possible solutions using an intuitive set of parameters that define the redundancy of the system.

N.I. Badler, D.N. Metaxas, G. Huang, A. Goswami, S. Huh,
Dynamic simulation for zero-gravity activities,
Aviation, Space, and Environment Medicine Journal, 2000.
(pdf).

Abstract:
Working and training for space activities is difficult in terrestrial environments. We approach this crucial aspect of space human factors through 3D computer graphics dynamics simulation of crewmembers, their tasks, and physics-based movement modeling. Such virtual crewmembers may be used to design tasks and analyze their physical workload to maximize success and safety without expensive physical mockups or partially realistic neutral-buoyancy tanks. Among the software tools we have developed are methods for fully articulated 3D human models and dynamic simulation. We are developing a fast recursive dynamics algorithm for dynamically simulating articulated 3D human models, which comprises kinematic chains -- serial, closed-loop, and tree-structure -- as well as the inertial properties of the segments. Motion planning is done by first solving the inverse kinematic problem to generate possible trajectories, and then by solving the resulting nonlinear optimal control problem. For example, the minimization of the torques during a simulation under certain constraints is usually applied and has its origin in the biomechanics literature. Examples of space activities shown are zero-gravity self orientation and ladder traversal. Energy expenditure is computed for the traversal task.

A. Goswami and M. Peshkin,
Mechanically implementable accommodation matrices for passive force control,
International Journal of Robotics Research, Vol. 18, No. 8, 1999.
(pdf).

Abstract:
Robot force control implemented by means of passive mechanical devices has inherent advantages over active implementations with regard to stability, response rapidity, and physical robustness. The class of devices considered in this paper consists of a Stewart platform-type mechanism interconnected with a network of adjustable mechanical elements such as springs and dampers. The control law repertoire of such a device, imagined as a robot wrist, is given by the range of admittance matrices that it may be programmed to possess. This paper focuses on wrists incorporating damper networks for which the admittance matrices reduce to accommodation or inverse-damping matrices.

We show that a hydraulic network of fully adjustable damper elements may attain any diagonally dominant accommodation matrix. We describe the technique of selecting the individual damping coefficients to design a desired matrix. We identify the set of dominant matrices as a polyhedral convex cone in the space of matrix entries, and show that each dominant matrix can be composed of a positive linear combination of a fixed set of basis matrices.

The overall wrist-accommodation matrix is obtained by projecting the accommodation matrix of the damper network through the wrist kinematics. The linear combination of the dominant basis matrices projected through the wrist kinematics generates the entire space of mechanically implementable force-control laws. We quantify the versatility of mechanically implementable force-control laws by comparing this space to the space of all matrices.

A. Goswami,
Postural stability of biped robots and the foot rotation indicator (FRI) point,
International Journal of Robotics Research, Vol. 18, No. 6, 1999.
(pdf).

Abstract:
The focus of this paper is the problem of foot rotation in biped robots during the single-support phase. Foot rotation is an indication of postural instability, which should be carefully treated in a dynamically stable walk and avoided altogether in a statically stable walk. We introduce the foot-rotation indicator (FRI) point, which is a point on the foot/ground-contact surface where the net groundreaction force would have to act to keep the foot stationary. To ensure no foot rotation, the FRI point must remain within the convex hull of the foot-support area.

In contrast with the ground projection of the center of mass (GCoM), which is a static criterion, the FRI point incorporates robot dynamics. As opposed to the center of pressure (CoP)—better known as the zero-moment point (ZMP) in the robotics literature—which may not leave the support area, the FRI point may leave the area. In fact, the position of the FRI point outside the footprint indicates the direction of the impending rotation and the magnitude of rotational moment acting on the foot. Owing to these important properties, the FRI point helps not only to monitor the state of postural stability of a biped robot during the entire gait cycle, but indicates the severity of instability of the gait as well. In response to a recent need, the paper also resolves the misconceptions surrounding the CoP/ZMP equivalence.

A. Goswami, B. Thuilot, and B. Espiau,
A study of the passive gait of a compass-like biped robot: symmetry and chaos,
International Journal of Robotics Research, Vol. 17, No. 12, 1998.
(pdf).

Abstract:
The focus of this work is a systematic study of the passive gait of a compass-like, planar, biped robot on inclined slopes. The robot is kinematically equivalent to a double pendulum, possessing two kneeless legs with point masses and a third point mass at the "hip" joint. Three parameters, namely, the ground-slope angle and the normalized mass and length of the robot describe its gait. We show that in response to a continuous change in any one of its parameters, the symmetric and steady stable gait of the unpowered robot gradually evolves through a regime of bifurcations characterized by progressively complicated asymmetric gaits, eventually arriving at an apparently chaotic gait where no two steps are identical. The robot can maintain this gait indefinitely.

A necessary (but not sufficient) condition for the stability of such gaits is the contraction of the "phase-fluid" volume. For this frictionless robot, the volume contraction, which we compute, is caused by the dissipative effects of the ground-impact model. In the chaotic regime, the fractal dimension of the robot’s strange attractor (2.07) compared to its state-space dimension (4) also reveals strong contraction.

We present a novel graphical technique based on the first return map that compactly captures the entire evolution of the gait, from symmetry to chaos. Additional passive dissipative elements in the robot joint result in a significant improvement in the stability and the versatility of the gait, and provide a rich repertoire for simple control laws..

(Among other contributions to the study of compass gait, this paper used the phase space representation of limit cycle which is ubiquitous now. Also this paper used Liouville Theorem (1838) to prove the stability of a limit cycle exhibited by the a simple robot. The method used is the contraction of an elementary phase space volume as it flows. This technique, used in the hybrid compass-gait system, is similar to the "contraction theory" popularized by Jean-Jacques Slotine.)

A. Goswami,
A new gait parameterization technique by means of cyclogram moments: Application to human slope walking,
Gait & Posture, Vol. 8, No. 1, 1998.
(pdf).

Abstract:
A new parameterization technique for the systematic characterization of human walking gait in diverse external conditions is proposed in this work. By parameterization we mean a quantitative expression of certain gait descriptors as the function of an external parameter, such as the ground slope. The mathematical quantities derived from the geometric features of the hip-knee cyclograms are the main gait descriptors considered in this study. We demonstrate that these descriptors, expressed in a general setting as the geometric moments of the cyclogram contours, can meaningfully reflect the evolution of the gait kinematics on different slopes. We provide a new interpretation of the cyclogram perimeter and discover two potential invariants of slope-walking gait. Experimental slope-walking data obtained at 1 degree interval within the range of -13 deg to +13 deg (+/- 23) on a variable-inclination treadmill was used in this study.

The parameterization procedure presented here is general in nature and may be employed without restriction to any closed curve such as the phase diagram, the moment-angle diagram, and the velocity-velocity curves of human gait. The technique may be utilized for the quantitative characterization of normal gait, global comparison of two different gaits, clinical identification of pathological conditions and for the tracking of progress of patients under rehabilitation program.

A. Goswami, B. Espiau, and A. Keramane,
Limit cycles in a passive compass gait biped and passivity-mimicking control laws,
Journal of Autonomous Robots, Vol. 4, No. 3, 1997.
(pdf).

T. C. Kienzle III, S. D. Stulberg, M. A. Peshkin, A. Quaid, J. Lea, A. Goswami, and C-H Wu
Computer-assisted total knee replacement surgical system using a calibrated robot,
IEEE Engineering in Medicine and Biology, May/June, 1995.
(pdf).

A. Goswami and J. R. Bosnik,
On a relationship between the physical features of robotic manipulators and the kinematic parameters produced by numerical calibration,
ASME Journal of Mechanical Design, December 1993.

Book Sections and Reports

S-H. Lee and A. Goswami,
The reaction mass pendulum (RMP) model for humanoid robot gait and balance control,
Humanoid Robots (Editor: Ben Choi), (In-Tech), Austria, February 2009.
(pdf).

Ambarish Goswami and E. Cordier,
Moment-based parameterization of evolving cyclograms on gradually changing slopes,
Computer Methods in Biomechanics & Biomedical Engineering, v.2, Middleton J., Jones M.L. and Pande G.N. Eds.
Gordon and Breach Science Publishers, 1998.

Thomas C. Kienzle III, S. David Stulberg, Michael Peshkin, Arthur Quaid, Jon Lea, Ambarish Goswami,
A Computer-assisted total knee replacement surgical system using a calibrated robot,
in Computer Assisted Surgery, edited by Russell H. Taylor, Stephane Lavallee, Grigore Burdea, and Ralph Moesges.
MIT Press, 1996.

A. Goswami, B. Thuilot, and B. Espiau,
Compass-like biped robot Part I: Stability and bifurcation of passive gaits,
INRIA Research Report No. 2996, October 1996.
(download).

Abstract:
It is well-known that a suitably designed unpowered mechanical biped robot can «walk» down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, step period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. The energy required to maintain the steady motion comes from the conversion of the biped's gravitational potential energy as it descends. Investigation of such passive «natural» motions may potentially lead us to strategies useful for controlling active walking machines as well as to understand human locomotion. In this report we demonstrate the existence and the stability of symmetric and asymmetric passive gaits using a simple nonlinear biped robot model. Kinematically the robot is identical to a double pendulum (similar to the Acrobot and the Pendubot) and is able to walk with the so-called compass gait. We also identify period-doubling bifurcation in this passive gait which eventually leads to a chaotic regime for larger slopes.

A. Goswami,
Mechanical computation for passive force control,
Ph.D. Thesis, Northwestern University, 1993.

A. Goswami,
Analysis of the relationship between the physical and the mathematical kinematic parameters in robotic manipulator parameter estimation algorithms,(without figures, sorry!)
M.S. Thesis, Drexel University, 1989.
(pdf).

Abstract: Although kinematic parameter estimation is well-established as a technique for improving end effector positioning accuracy of a robotic manipulator, little attention has been given to the relationship between the optimal mathematical parameters and the corresponding physical parameters of the manipulator. Such a relationship is very much desirable from the standpoint of preventive maintenance and isolation of sources of damage in the manipulator body. In this work, choice of kinematic model is shown to have a strong effect on this relationship, as well as on the calibration process in general. It is observed that the most desirable kinematic model for a given manipulator includes redundant parameters, which interact numerically among themselves during the solution process and complicate interpretation of results. A kinematic model with no redundant parameter, on the other hand, contains too few parameters to get a comprehensible relation between the physical dimensions of the manipulator and the mathematical parameters. Multiple point data collection in a single posture is shown to be of no significant help in preserving the mathematical/physical parameter relationship.

Refereed Conference Proceedings

S-H. Lee and A. Goswami,
Ground reaction force control at each foot: A momentum-based humanoid balance controller for non-level and non-stationary ground,
IROS 2010, Taipei, Taiwan, October 2010.
(pdf).

Abstract:
We present a novel momentum-based method for maintaining balance of humanoid robots. By controlling the desired ground reaction force (GRF) and center of pressure (CoP) at each support foot, our method can naturally deal with non-level and non-stationary ground at each foot-ground contact, as well as different frictional properties. We do not make use of the net GRF and CoP which may be difficult or impossible to compute for non-level grounds. Our method minimizes the ankle torques during double support. We show the effectiveness of this new balance control method by simulating various experiments with a humanoid robot including maintaining balance when two feet are on separate moving supports with different inclinations and velocities.

A. Dutta and A. Goswami
Human postural model that captures rotational inertia,
The 33rd Annual Meeting of the American Society of Biomechanics ASB 2010, Providence, Rhode Island, USA, August, 2010.
(pdf).

Abstract:
Inverted pendulum models have been very beneficial for the modeling and analysis of human gait and balance. These reduced models allow us to ignore the movements of the individual limbs, and instead, focus on two important points ¬-- the center of pressure (CoP) and the center of mass (CoM) -- and the lean line that connects the two points. A limitation of the existing reduced models is that they represent the entire human body only as a point mass and do not characterize its moment of inertia. The rotational inertia is a property of the distributed masses of the limbs, and by ignoring it, un-natural constraints, such as zero angular momentum at the CoM and resultant ground reaction force (GRF) collinear with the lean line, are forced on to the model.

The Reaction Mass Pendulum (RMP) model extends the existing models by replacing the point mass with an extended rigid body -- the abstracted 3D reaction mass -- that characterizes the aggregate rotational inertia of the subject projected at the CoM. As the person moves through different limb configurations, the centroidal moment of inertia continuously changes, which is captured by the changing shape, size and orientation of the ellipsoidal reaction mass. We postulate that analysis of the rotational inertia especially in cases of pathological gait can provide additional insight. This is demonstrated with normative gait data from four able-bodied subjects and pathological gait data from one spinal cord injured subject.

S. Kalyanakrishnan and A. Goswami
Predicting falls of a humanoid robot through machine learning,
IAAI-10, Atlanta, Georgia, USA, July, 2010.
(pdf).

Abstract:
Although falls are undesirable in humanoid robots, they are also inevitable, especially as robots get deployed in physically interactive human environments. We consider the problem of "fall prediction", i.e., to predict if a robot's balance controller can prevent a fall from the current state. A trigger from the fall predictor is used to switch the robot from a balance maintenance mode to a fall control mode. Hence, it is desirable for the fall predictor to signal imminent falls with sufficient lead time before the actual fall, while minimizing false alarms. Analytical techniques and intuitive rules fail to satisfy these competing objectives on a large robot that is subjected to strong disturbances and exhibits complex dynamics.

Today effective supervised learning tools are available for finding patterns in high-dimensional data. Our paper contributes a novel approach to engineer fall data such that a supervised learning method can be exploited to achieve reliable prediction. Specifically, we introduce parameters to control the tradeoff between the false positive rate and lead time. Several parameter combinations yield solutions that improve both the false positive rate and the lead time of hand-coded solutions. Learned predictors are decision lists with typical depths of 5-10, in a 16-dimensional feature space. Experiments are carried out in simulation on an Asimo-like robot.

U. Nagarajan and A. Goswami
Generalized Direction Changing Fall Control of Humanoid Robots Among Multiple Objects,
ICRA 2010, Anchorage, Alaska, USA, May 2010.
(pdf).

Abstract:
Humanoid robots are expected to share human environments in the future and it is important to ensure safety of their operation. A serious threat to safety is the fall of a humanoid robot, which can seriously damage both the robot and objects in its surrounding. This paper proposes a strategy for planning and control of fall. The controller's objective is to prevent the robot from hitting surrounding objects during a fall by modifying its default fall direction.

We have earlier presented such a direction-changing fall controller, see here in ICRA 2009. However, the controller was applicable only when the robot's surrounding contained a single object. In this paper we introduce a generalized approach to humanoid fall-direction control among multiple objects. This new framework algorithmically establishes a desired fall direction through assigned scores, considers a number of control options, and selects and executes the best strategy. The fall planner is also able to select ``No Action" as the best strategy, if appropriate. The controller is interactive and is applicable for fall occurring during upright standing or walking. The fall performance is continuously tracked and can be improved in real-time. The planning and control algorithms are demonstrated in simulation on an ASIMO-like humanoid robot.

S.-K. Yun, A. Goswami and Y. Sakagami,
Safe Fall: Humanoid robot fall direction change through intelligent stepping and inertia shaping,
ICRA 2009, Kobe, Japan, May 2009.
(pdf).

Abstract:
Although fall is a rare event in the life of a humanoid robot, we must be prepared for it because its consequences are serious. In this paper we present a fall strategy which rapidly modifies the robot's fall direction in order to avoid hitting a person or an object in the vicinity. Our approach is based on the key observation that during "toppling" the rotational motion of a robot necessarily occurs at the leading edge or the leading corner of its support base polygon. To modify the fall direction the robot needs to change the position and orientation of this edge or corner vis-a-vis the prohibited direction. We achieve it through intelligent stepping as soon as a fall is detected. We compute the optimal stepping location which results in the safest fall. Additional improvement to the fall controller is achieved through inertia shaping techniques aimed at controlling the centroidal inertia of the robot.

We demonstrate our results through the simulation of an Asimo-like humanoid robot. To our knowledge, this is the first implementation of a controller that attempts to change the fall direction of a humanoid robot.

S. Stramigioli, Vincent Duindam, Gijs van Oort, and A. Goswami,
Compact Analysis of 3D Bipedal Gait Using Geometric Dynamics of Simplified Models,
ICRA 2009, Kobe, Japan, May 2009.
(pdf).

Abstract:
The large number of degrees of freedom in legged robots give rise to complicated dynamics equations. Analyzing these equations or using them for control can therefore be a difficult and non-intuitive task. A simplification of the complex multi-body dynamics can be achieved by instantaneously reducing it to an equivalent single inertial entity called the locked inertia or the composite rigid body inertia.

In this paper, we adopt the methods of geometric dynamics to analyze the gait using the locked inertia of the robot. The analysis includes the rolling of a biped on a 3D rigid foot and 3D impacts. An example of numerical optimization of foot shape parameters is shown.

Our long-term objective is to develop the theoretical framework and to provide the necessary tools for systematic analysis, design, and control of efficient biped robots.

A. Goswami,
Kinematic and dynamic analogies between planar biped robots and the reaction mass pendulum (RMP) model,
Humanoids 2008, Daejeon, Korea, December 2008.
(pdf).

Abstract:
In order to simplify dynamic analysis, humanoid robots are often abstracted with various versions of the inverted pendulum model. However, most of these models do not explicitly characterize the robot's rotational inertia, a critical component of its dynamics, and especially of its balance. To remedy this, we have earlier introduced the \textit{Reaction Mass Pendulum (RMP)}, an extension of the inverted pendulum, which models the rotational inertia and angular momentum of a robot through its centroidal composite rigid body (CCRB) inertia. However, we presented only the kinematic mapping between a robot and its corresponding RMP.

Focussing in-depth on planar mechanisms, here we derive the dynamic equations of the RMP and explicitly compute the parameters that it must possess in order to establish equivalence with planar compass gait robot. In particular, we show that, a) an angular momentum equality between the robot and RMP does not necessarily guarantee kinetic energy equality, and b) a cyclic robot gait may not result in a cyclic RMP movement.

The work raises the broader question of how quantitatively similar the simpler models of humanoid robot must be in order for them to be of practical use.

D. Orin and A. Goswami,
Centroidal Momentum Matrix of a Humanoid Robot: Structure and Properties,
IROS 2008, Nice, France, September 2008.
(pdf).

Abstract:
The centroidal momentum of a humanoid robot is the sum of the individual link momenta, after projecting each to the robot's Center of Mass (CoM). Centroidal momentum is a linear function of the robot's generalized velocities and the Centroidal Momentum Matrix is the matrix form of this function. This matrix has been called both a Jacobian matrix and an inertia matrix by others. We show that it is actually a product of a Jacobian and an inertia matrix.

We establish the relationship between the Centroidal Momentum Matrix and the well-known joint-space inertia matrix. We present a Transformation Diagram that graphically captures the inter-relationships of the matrix operators and motion and momentum variables in Joint Space, CoM Space as well as the System Space.

The Centroidal Momentum Matrix is a local scaling function that maps the joint rates to the centroidal momentum. Following the concept of the manipulability ellipsoid, we propose the centroidal momentum ellipsoid that quantifies the momentum generation ability of the robot. We present a simulation plot showing the evolution of the singular values of the Centroidal Momentum Matrix during the walking motion of a humanoid.

J. Rebula, J. Pratt, F Canas, and A. Goswami,
Learning Capture Point for Improved Humanoid Push Recovery,
Humanoids07, Pittsburgh, PA, November-December 2007.
(pdf).

Abstract:
We present a method for learning Capture Points for humanoid push recovery. A Capture Point is a point on the ground to which the biped can step and stop without requiring another step. Being able to predict the location of such points is very useful for recovery from significant disturbances, such as after being pushed. While dynamic models can be used to compute Capture Points, model assumptions and modeling errors can lead to stepping in the wrong place, which can result in large velocity errors after stepping.We present a method for computing Capture Points by learning offsets to the Capture Points predicted by the Linear Inverted Pendulum Model, which assumes a point mass biped with constant Center of Mass height. We validate our method on a three dimensional humanoid robot simulation with 12 actuated lower body degrees of freedom, distributed mass, and articulated limbs. Using our learning approach, robustness to pushes is significantly improved as compared to using the Linear Inverted Pendulum Model without learning.
Download animations:
Robot performance before learning
Robot performance after learning

Gabriel Aguirre-Ollinger, J. Edward Colgate, Michael A. Peshkin, and A. Goswami,
A 1-DOF Assistive Exoskeleton with Virtual Negative Damping: Effects on the Kinematic Response of the Lower Limbs,
IROS 2007, San Diego, CA.
(pdf).

Abstract:
We propose a novel control method for lowerlimb assist that produces a virtual modification of the mechanical impedance of the human limbs. This effect is accomplished through the use of an exoskeleton that displays active impedance. The proposed method is aimed at improving the dynamic response of the human limbs, while preserving the user’s control authority. Our goal is to use active-impedance exoskeleton control to improve the user’s agility of motion, for example by reducing the average time needed to complete a movement.

Our control method has been implemented in a 1-DOF exoskeleton designed to assist human subjects performing knee flexions and extensions. In this paper we discuss an initial study on the effect of negative exoskeleton damping (a particular case of active-impedance control) on the subject’s time to complete a target-reaching motion. Experimental results show this effect to be statistically significant. On average, subjects were able to reduce the time to complete the motion by 16%.

Gabriel Aguirre-Ollinger, J. Edward Colgate, Michael A. Peshkin, and A. Goswami,
Active impedance control of a lower-limb assistive exoskeleton,
10th Int. Conf. on Rehabilitation Robotics (ICORR'07), Noordwijk, the Netherlands, Jun 13-15 2007.
(pdf).

Abstract:
We propose a novel control method for lower-limb assist that produces a virtual modification of the mechanical impedance of the human limbs. This effect is accomplished by making the exoskeleton display active impedance properties. Active impedance control emphasizes control of the exoskeleton’s dynamics and regulation of the transfer of energy between the exoskeleton and the user. Its goal is improving the dynamic response of the human limbs without sacrificing the user’s control authority. The proposed method is an alternative to myoelectrical exoskeleton control, which is based on estimating muscle torques from electromyographical (EMG) activity. Implementation of an EMG-based controller is a complex task that involves modeling the user's musculoskeletal system and requires recalibration. In contrast, active impedance control is less dependent on estimation of the user's attempted motion, thereby avoiding conflicts resulting from inaccurate estimation.

In this paper we also introduce a new form of human assist based on improving the kinematic response of the limbs. Reduction of average muscle torques is a common goal of research in human assist. However, less emphasis has been placed so far on improving the user’s agility of motion. We aim to use active impedance control to attain such effects as increasing the user's average speed of motion, and improving their acceleration capabilities in order to compensate for perturbations from the environment.

S-H. Lee and A. Goswami,
Reaction Mass Pendulum (RMP): An explicit model for centroidal angular momentum of humanoid robots,
IEEE Int. Conf. on Robotics and Automation, Rome, Italy, April 2007.
(pdf).

Abstract:
A number of conceptually simple but behaviorrich “inverted pendulum” humanoid models have greatly enhanced the understanding and analytical insight of humanoid dynamics. However, these models do not incorporate the robot’s angular momentum properties, a critical component of its dynamics. We introduce the Reaction Mass Pendulum (RMP) model, a 3D generalization of the better-known reaction wheel pendulum. The RMP model augments the existing models by compactly capturing the robot’s centroidal momenta through its composite rigid body (CRB) inertia. This model provides additional analytical insights into legged robot dynamics, especially for motions involving dominant rotation, and leads to a simpler class of control laws. In this paper we show how a humanoid robot of general geometry and dynamics can be mapped into its equivalent RMP model. A movement is subsequently mapped to the time evolution of the RMP. We also show how an “inertia shaping” control law can be designed based on the RMP.

Kangkang Yin contributed an important correction to the above paper. (Correction)
Download animations:
HOAP2 Sumo motion with simultaneous RMP
Fujitsu HOAP2 gait with simultaneous RMP

J. Pratt, J. Carff, S. Drakunov and A. Goswami,
Capture Point: A Step toward Humanoid Push Recovery,
Humanoids2006, Genoa, Italy, December 2006.
(pdf).

Abstract:
It is known that for a large magnitude push a human or a humanoid robot must take a step to avoid a fall. Despite some scattered results, a principled approach towards “When and where to take a step” has not yet emerged. Towards this goal, we present methods for computing Capture Points and the Capture Region, the region on the ground where a humanoid must step to in order to come to a complete stop. The intersection between the Capture Region and the Base of Support determines which strategy the robot should adopt to successfully stop in a given situation.

Computing the Capture Region for a humanoid, in general, is very difficult. However, with simple models of walking, computation of the Capture Region is simplified. We extend the wellknown Linear Inverted Pendulum Model to include a flywheel body and show how to compute exact solutions of the Capture Region for this model. Adding rotational inertia enables the humanoid to control its centroidal angular momentum, much like the way human beings do, significantly enlarging the Capture Region.

We present simulations of a simple planar biped that can recover balance after a push by stepping to the Capture Region and using internal angular momentum. Ongoing work involves applying the solution from the simple model as an approximate solution to more complex simulations of bipedal walking, including a 3D biped with distributed mass.
Download animations:
Push recovery with lunge only
Push recovery under increasing forward pushes
Push recovery under forward and lateral pushes

M. Abdallah and A. Goswami,
A biomechanically motivated two-phase strategy for biped upright balance control,
IEEE Int. Conf. on Robotics and Automation, Barcelona, Spain, April 2005.
(pdf).

Abstract:
Balance maintenance and upright posture recovery under unexpected environmental forces are key requirements for safe and successful co-existence of humanoid robots in normal human environments. In this paper we present a two-phase control strategy for robust balance maintenance under a force disturbance. The first phase, called the reflex phase, is designed to withstand the immediate effect of the force. The second phase is the recovery phase where the system is steered back to a statically stable “home” posture. The reflex control law employs angular momentum and is characterized by its counter-intuitive quality of “yielding” to the disturbance. The recovery control employs a general scheme of seeking to maximize the potential energy and is robust to local ground surface feature. Biomechanics literature indicates a similar strategy in play during human balance maintenance.
Download animations:
Recovery under potential energy control
Reflex and recovery against a 300N horizontal force
Robot balancing on a swaying table

R. C. Browning, J. Modica, R. Kram and A. Goswami,
The effects of added leg mass on the biomechanics and energetics of walking,
American Society of Biomechanics (ASB), April 2004.
(pdf).

A. Goswami and V. Kallem,
Rate of change of angular momentum and balance maintenance of biped robots,
IEEE Int. Conf. on Robotics and Automation, New Orleans, April 2004.
(pdf).

Abstract:
In order to engage in useful activities upright legged creatures must be able to maintain balance. Despite recent advances, the understanding, prediction and control of biped balance in realistic dynamical situations remain an unsolved problem and the subject of much research in robotics and biomechanics. Here we study the fundamental mechanics of rotational stability of multi-body systems with the goal to identify a general stability criterion. Our research focuses on the rate of change of centroidal angular momentum of a robot, as the physical quantity containing its stability information. We propose three control strategies using angular momentum that can be used for stability recapture of biped robots. For free walk on horizontal ground, a derived criterion refers to a point on the foot/ground surface of a robot where the total ground reaction force would have to act such that angular momentum rate change = 0. This new criterion generalizes earlier concepts such as GCoM, CoP, ZMP, and FRI point, and extends their applicability.

A. Goswami,
Kinematic quantification of gait symmetry based on bilateral cyclograms,
XIXth Congress of the International Society of Biomechanics (ISB), Dunedin, New Zealand, July 2003.
(paper pdf)
(poster pdf).

Abstract:
Symmetry is considered to be an important indicator of healthy gait and a lack of symmetry the effect of various pathologies. Information on gait symmetry can be instrumental in clinical diagnosis, decision-making and for tracking the progress of rehabilitation procedures.

We introduce a system of new gait symmetry measures that are derived from the geometric properties of bilateral cyclograms (also called angle-angle diagrams). The symmetry measures are simple, physically meaningful, objective, reliable and well suited for statistical study. We compute the symmetry measures for gaits in both non-paretic (healthy) and hemiparetic subjects and demonstrate how they can be used to characterize normal gait and identify and quantify gait asymmetry.

S. Goldenstein, M. Karavelas, D. Metaxas, L. Guibas and A. Goswami,
Scalable Dynamical Systems for Multi-Agent Steering and Simulation,
IEEE Int. Conf. on Robotics and Automation, Seoul, Korea, May 2001.
(pdf).

A. Goswami,
Segmentation of biomechanical signals by joint-space distance criterion,
17th Congress of the International Society of Biomechanics (ISB), Calgary, Canada, August 1999.
(pdf).

H. Sun, A. Goswami, D. Metaxas,
Cyclogram planarity is preserved in upward slope walking,
17th Congress of the International Society of Biomechanics (ISB), Calgary, Canada, August 1999.
(Download from Harold Sun's website).

A. Goswami,
Foot rotation indicator (FRI) point: A new gait planning tool to evaluate postural stability of biped robots,
IEEE Int. Conf. on Robotics and Automation, Detroit, May 1999, pp.47-52.
(pdf).
L. Roussel, C. Canudas de Wit, and A. Goswami,
Generation of energy-optimal complete gait cycles for biped robots,
IEEE Int. Conf. on Robotics and Automation, Leuven, Belgium, May 1998.
(pdf).

Abstract:
In this paper we address the problem of energy optimal gait generation for biped robots Using a sim plied robot dynamics that ignores the eects of cen tripetal forces we obtain unconstrained optimal tra jectories generated by piecewise constant inputs We study a complete gait cycle comprising single support double support and the transition phases The energy optimal gaits for dierent step lengths and velocities are compared with natural human gait.

M. Mata-Jimenez, B. Brogliato, and A. Goswami,
On the control of mechanical systems with dynamic backlash,
CDC Conf, San Diego, CA, December 1997.
(pdf).
M. Mata-Jimenez, B. Brogliato, and A. Goswami,
Analysis of PD control of mechanical systems with dynamic backlash,
2nd Int. Symp. MV2 on Active Control in Mechanical Engineering, Lyon, France, October 1997.
(pdf).

C. Canudas de Wit, L. Roussel, and A. Goswami,
Periodic stabilization of a 1-dof hopping robot over nonlinear compliant surface,
IFAC Symp. on Robot Control (SyRoCo), Nantes, France, September 1997.
(pdf).
A. Goswami and E. Cordier,
Moment-based parameterization of cyclograms of slope-walking,
XVIth Congress of the Int. Society of Biomechanics, Tokyo, Japan, August 1997
(finalist for the Best Young Investigator award).
(pdf).

B. Espiau and the BIP team,
BIP: A joint project for the development of an anthropomorphic biped robot,
8th Int. Conf. on Advanced Robotics (ICAR), Monterey, CA, July 1997..
C. Canudas de Wit, L. Roussel, and A. Goswami,
Comparative study of methods for energy-optimal gait generation for biped robots,
Int. Conf. on Informatics and Control, St. Petersburg, Russia, June 1997.
(pdf).

Abstract:
In this paper we compare three methods for the energy optimal gait gener ation for biped robots during the single support phase The rst approach searches for unconstrained trajectories generated by piecewise constant inputs the second approach constrains the Cartesian trajectories of the swing foot and the hip of the robot to a class of timepolynomial functions and the last method approximates the robot joint trajectories by a truncated Fourier frequency series Using a simplied robot dynamics that ignore the centripetal and Coriolis terms these methods are compared according to the input energy and the initial mechanical energy The numerical study presented here shows that for an equivalent amount of computational burden the unconstrained method provides motions with the lowest input energy Furthermore it also provides the initial velocities that generate ballistic motions with almost zero input energy.

E. Cordier, A. Goswami, and M. Bourlier,
Kinematic parameterization of natural slope walking,
13th Int. Symp. on ``Posture and Gait'', Paris, France, June 1997..
(pdf).
A. Goswami and E. Cordier,
Moment-based parameterization of evolving cyclograms on gradually changing slopes,
3rd Int. Symp. on Computer Methods in Biomechanics & Biomedical Engr, Barcelona, May, 1997.
(pdf).
B. Thuilot, A. Goswami, and B. Espiau,
Bifurcation and chaos in a simple passive bipedal gait,
IEEE Int. Conf. on Robotics and Automation, Albuquerque, NM, April 1997.
(pdf).

Abstract:
This paper proposes an analysis of the behavior of perhaps the simplest biped robot the compass gait model It has been shown previously that such a robot can walk down a slope indenitely without any actua tion Passive motions of this nature are of particular interest since they may lead us to strategies for con trolling active walking machines as well as to a better understanding of human locomotion We show here that depending on the parameters of the system pas sive compass gait may exhibit 1-periodic 2^n periodic and chaotic gaits proceeding from cascades of period doubling bifurcations Since compass equations are quite involved (they combine nonlinear dierential and algebraic equations in a 4-dimensional space) our in vestigations rely in part on numerical simulations.

K. Kedzior, A. Morecki, M. Wojtyra, T. Zagrajek, T. Zielinska, A. Goswami, M. Waldron, and K. Waldron,
Development of a mechanical simulation of human walking,
ROMANSY, Udine, Italy, July 1996..

A. Goswami, B. Espiau, and A. Keramane,
Limit cycles and their stability in a passive bipedal gait,
IEEE Int. Conf. on Robotics and Automation, Minneapolis, MN, April 1996.
(The signature phase diagram of a compass gait robot that we frequently encounter now, was first introduced in this paper.).
(pdf).

Abstract:
It is wellknown that a suitably designed unpowered mechanical biped robot can walk down an inclined plane with a steady gait The characteristics of the gait eg velocity time period step length depend on the geometry and the inertial properties of the robot and the slope of the plane A passive motion has the distinction of being natu ral and is likely to enjoy energy optimality Investiga tion of such motions may potentially lead us to strate gies useful for controlling active walking machines In this paper we demonstrate that the nonlinear dy namics of a simple passive "compass gait" biped robot can exhibit periodic and stable limit cycle Kinemat ically the robot is identical to a double pendulum (or its variations such as the Acrobot and the Pendubot) Simulation results also reveal the existence of a sta ble gait with unequal step lengths We also present an active control scheme which enlarges the basin of attraction of the passive limit cycle.

A. Goswami, J. T. Lea, A. Quaid, M. A. Peshkin, T. C. Kienzle III, and S. D. Stulberg,
Achieving surgical accuracy with robots using parameter identification,
First Medical Robotics and Computer Assisted Surgery (MRACS) Symposium, Pittsburgh, PA, 1994.

B. Espiau and A. Goswami,
Compass gait revisited,
IFAC Symp. on Robot Control (SyRoCo), Capri, Italy, September 1994.
(pdf).

M. A. Peshkin, A. Goswami, and J. M. Schimmels,
Force-guided assembly,
31st Annual Allerton Conf. on Communication, Control, and Computing, Urbana-Champaign, IL, October 1993..

A. Goswami and M. A. Peshkin,
Task-space/joint-space damping transformations for passive redundant manipulators,
IEEE Int. Conf. on Robotics and Automation (invited session), Atlanta, GA, April 1993.
(pdf).

Abstract:
We consider here passive mechanical wrists, capable of imparting a desired damping matrix to a grasped workpiece. Previous work has shown how to select a damping matrix such that an assembly operation can be made force-guided. The passive mechanical wrist is to be programmaable - it can adopt a wide range of damping matrices - by virtue of a number of tunable dampers which inrcrconnect the joints. We have been studying the range of damping matrices that such a wrist can adopt, purely by tuning its dampers. We find that a redundant wrist has a broader range of realizable damping matrices than a non-redundant wrist. A kinematic Jacobian relates the task-space damping matrix to a similar matrix in the hydraulic space of the tunable dampers (joint- space). For redudundant wrists the transformation of damping matrices between task-space and joint-space is not straightforward. In this paper we identify the causal directions along which the transformations are linear. We show that the joint-space matrices which are obtained as linear tranrfonnations of desired task-space matrices are all singular. Many realizable joint-space matrices (corresponding to a desired task-space damping matrix) are shown to exist which are not discovered by linear transformations.

A. Goswami and M. A. Peshkin,
Mechanical computation for passive force control,
IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, April 1993.
(pdf).

Abstract:
Force control implemented by a passive mechanical device (perhaps a wrist) has inherent advantages over active implementations. A passive mechanical device can regain some of the versatility of its active counterpart if it incorporates mechanical elements with programmable parameters, e.g. damping coefficients or spring stiffnesses. We wish to characterize the range of accommodation matrices that a passive device may be programmed to possess. Here we review the known theoretical limits on the accommodation (inverse damping) matrices that any linear system of programmable dampers may adopt. Recent results [22, 26] show that such matrices are well suited to force-guided assembly. However, even with fully adjustable damping constants a mechanical device of fixed geometric design can attain only a subset of the all accommodation matrices. In this work we describe the set of attainable accommodation matrices, and show that each such matrix can be composed of a positive linear combinations of a fixed set of basis matrices. We show how the damping coefficients can be chosen to achieve a desired accommodation matrix, i.e. how to program this mechanical computer. We compare the space of attainable matrices to the space of all matrices, and suggest a method of visualizing it in low-dimensional examples.

A. Goswami, A. Quaid, and M. A. Peshkin,
Complete parameter identification of a robot using partial pose information,
IEEE Int. Conf. on Robotics and Automation, Atlanta, GA, April 1993.
(pdf).

Abstract:
The absolute accuracy of a robot depends to a large extent on the accuracy with which its kinematic parameters are known. Many methods have been explored for inferring the kinematic parameters of a robot from measurements taken as it moves. Some require an extemal global positioning system, usually optical or sonic. We have used instead a simple radial- distance linear transducer (LVDT) which measures the distance from a fmed point in the workspace to the robot's endpoint. This incomplete pose information is accumulated as the robot endpoint is moved within one or more spherical "shells" centered about the fmed point. Optimal values for all of the independent kinematic parameters of the robot can then be found Here we discuss the motivation, theory, implementation, and performance of this particularly easy calibration and parameter identification method We also address a recent disagreement in the literature about the class of measurements needed to fully i&ntifi a robot's kinematic parameters.

A. Goswami, A. Quaid, and M. A. Peshkin,
Calibration and parameter identification of a 6-DOF robot using a ball-bar system,
IEEE Int. Conf. on Systems, Man, and Cybernetics (invited session), Chicago, IL, September 1992..

A. Goswami and M. A. Peshkin,
Implementation of passive force control with redundant manipulators,
IEEE Int. Conf. on Systems, Man, and Cybernetics, Charlottesville, VA, October 1991.

A. Goswami and M. A. Peshkin,
A task-space formulation of passive force control,
IEEE Int. Symp. on Intelligent Control (invited session), Alexandria, VA, October 1991..

A. Goswami, M. A. Peshkin, and J. E. Colgate,
Passive robotics: An exploration of mechanical computation,
IEEE Int. Conf. on Robotics and Automation, Cincinnati, OH, April 1990 (Also in American Control Conference, San Diego, CA, invited session), May 1990.
(pdf).

Abstract:
We invite the reader to think of a passive wrist as a mechanical computer. The wrist computes a particular motion in response to every applied force, and this defines its control law. Suppose that the design of a wrist (the geometric layout of mechanical elements -- springs, hydraulic cylinders, dampers, and so on -- which compose it) is held fixed. We can "program" the wrist by changing the parameters (for example, the spring stiffnesses) of some of these elements. What is the range of control laws such a wrist can execute? The thesis of this paper is that a passive wrist, of fixed design, can be programmed to execute a wide range of useful control laws. We consider in particular wrists whose actuators are unpowered hydraulic cylinders, the ports of which are coupled to one another via variable-conductance constrictions. By selection of these conductances the wrist is programmed, much as an analog computer is programmed. We characterize mathematically the range of control laws such a device can compute..

A. Goswami and J. R. Bosnik,
Interpretation of redundant kinematic parameters in robotic manipulator calibration algorithms,
ASME Biennial Mechanisms Conference, Orlando, FL, September 1988.

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Page last updated August 28, 2010