Ambarish Goswami



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ASME Fellow 2013

Recent Seminars and Presentations:


Recent Papers:

  • Federico L. Moro, Michael Gienger, Ambarish Goswami, Nikos G. Tsagarakis and Darwin G. Caldwell
    An Attractor-based Whole-Body Motion Control (WBMC) System for Humanoid Robots
    Humanoids 2013, Atlanta, GA, October 2013.
    (pdf).

    Simulation video:
    Click Here


    Abstract:
    This paper presents a novel whole-body torquecontrol concept for humanoid walking robots. The presented Whole-Body Motion Control (WBMC) system combines several unique concepts. First, a computationally efficient gravity compensation algorithm for floating-base systems is derived. Second, a novel balancing approach is proposed, which exploits a set of fundamental physical principles from rigid multi-body dynamics, such as the overall linear and angular momentum, and a minimum effort formulation. Third, a set of attractors is used to implement movement features such as to avoid joint limits or to create end-effector movements. Superposing several of these attractors allows to generate complex wholebody movements to perform different tasks simultaneously. The modular structure of the proposed control system easily allows extensions. The presented concepts have been validated both in simulations, and on the 29-dofs compliant torque-controlled humanoid robot COMAN. The WBMC has proven robust to the unavoidable model errors.

    Features:


    Figure above:
    The behavior of the WBMC system is not always easy to predict. The torques generated by the MinEff (minimum effort) attractor in the case of a 2-link fixed-base robot, for instance, aim to bring the robot to a vertical position when gravity is the only external force acting on the robot, as shown in case (a) in the above figure. If another external force is applied as in case (b), instead, the MinEff locally searches for a configuration that minimizes all external disturbances. See the paper for other cases, c), d), and e), which are shown above.

    Figure above:
    We see snapshots from the video of the experimental validation of the WBMC with the COMAN robot (taken at 2Hz). In this case the robot configuration is perturbed by forcing the waist roll joint to change its angle. As the robot is released the MinEff (minimum effort) brings the robot back to a vertical, minimum effort configuration. The resulting motion is damped by the MomJ (joint moment) attractor, that prevents the velocity to grow uncontrolled.


  • D. Orin, A. Goswami and S.-H Lee,
    Centroidal Dynamics of a Humanoid Robot,
    Autonomous Robots, Vol. 35, No. 2, October 2013.
    (pdf).

    Simulation video:
    Click Here


    Abstract:
    The center of mass (CoM) of a humanoid robot occupies a special place in its dynamics. As the location of its effective total mass, and consequently, the point of resultant action of gravity, the CoM is also the point where the robot's aggregate linear momentum and angular momentum are naturally defined. The overarching purpose of this paper is to refocus our attention to centroidal dynamics: the dynamics of a humanoid robot projected at its CoM. In this paper we specifically study the properties, structure and computation schemes for the centroidal momentum matrix (CMM), which projects the generalized velocities of a humanoid robot to its spatial centroidal momentum. Through a transformation diagram we graphically show the relationship between this matrix and thewell-known joint-space inertia matrix. We also introduce the new concept of "average spatial velocity" of the humanoid that encompasses both linear and angular components and results in a novel decomposition of the kinetic energy. Further, we develop a very efficient O(N) algorithm, expressed in a compact form using spatial notation, for computing the CMM, centroidal momentum, centroidal inertia,and average spatial velocity. Finally, as a practical use of centroidal dynamics we show that a momentum-based balance controller that directly employs the CMM can significantly reduce unnecessary trunk bending during balance maintenance against external disturbance.

    Features:

    Centroidal Dynamics:
    The center of mass (CoM) of a humanoid robot is a uniquely important point in its dynamics. First of all, it is the effective location of the robot's total mass, and therefore, the point where its aggregate linear momentum is naturally defined. It is also the point through which the resultant gravity force acts. It should then come as no surprise that virtually all reduced humanoid models and control algorithms contain the CoM as an integral component.

    In the well-known example of a freely flying multi-link chain, the average behavior of the chain can be adequately described in terms of its CoM. While the dynamics of individual member links can be quite complex, the motion of the CoM follows a point-mass projectile profile which can be easily described and communicated. Additionally, the rotational motion of the aggregate chain obeys the conservation of angular momentum about the CoM or, the centroidal angular momentum. For many applications, such reduced description is instrumental in the analysis and control of the system.

    In a similar manner, surprisingly deep insight into the dynamics of a humanoid robot can be obtained simply by following the trajectory of its CoM, center of pressure (CoP), and the lean line connecting these two points. This has been known for a long time and has been utilized in the study of human motion. The study of humanoid dynamics has also inherited this trend and a number of progressively complex models, some of which are shown above, are currently used for analysis and control.

    Figure above:
    A number of progressively complex "inverted pendulum" models, which are currently used for the analysis and control of gait and balance of humanoid robots and humans.


    Transformation Diagram:



    Figure above:
    Transformation diagram showing the relations among the velocities and momenta of a robot. These vector quantities can be expressed in joint space, system space, or the CoM space of the robot. The matrices representing the linear transformations between velocities and momenta in different spaces are also shown in this diagram. The dashed line at the lower left of the diagram represents a minimum kinetic energy transformation, which is not a general transformation.

    Simulation:


    Figure above:
    We tested the momentum-based balance controller by simulating a humanoid robot model. In the simulation experiment the robot is subjected to a push from the lateral direction while standing on a narrow support, which is even slightly narrower than the width the robot's feet. In this environment, the robot must rotate its upper body in order to maintain balance, and our controller based on the centroidal momentum matrix (CMM) creates such a whole body motion in which the whole body segments including the trunk and arms are engaged to create the necessary admissible momentum rate change. We see a series of snapshots illustrating when the robot is subjected to an external push which is applied at the robot's CoM in the lateral direction from the robot's right side.


  • S.-H Lee and A. Goswami,
    Fall on Backpack: Damage Minimizing Humanoid Fall on Targeted Body Segment Using Momentum Control,
    Journal of Computational and Nonlinear Dynamics, Vol. 8, Issue 2, April 2013.
    (pdf).

    Simulation video:
    Click Here


    Abstract:
    Safety and robustness will become critical issues when humanoid robots start sharing human environments in the future. In physically interactive human environments, a catastrophic fall is a major threat to safety and smooth operation of humanoid robots. It is therefore imperative that humanoid robots be equipped with a comprehensive fall management strategy. This paper deals with the problem of reducing the impact damage to a robot associated with a fall. A common approach is to employ damage-resistant design and apply impact-absorbing material to robot limbs, such as the backpack and knee, that are particularly prone to fall related impacts. In this paper, we select the backpack to be the most preferred body segment to experience an impact. We proceed to propose a control strategy that attempts to re-orient the robot during the fall such that it impacts the ground with its backpack. We show that the robot can fall on the backpack even when it starts falling sideways. This is achieved by generating and redistributing angular momentum among the robot limbs through dynamic coupling. The planning and control algorithms for fall are demonstrated in simulation.


    Features:

    Simulation:


    Figure above (no controller):
    An external force applied at the CoM of the robot to its left makes the robot fall. The robot locks all the joints without triggering the fall controller. It falls sideways, and can get badly damaged.






    Figure above (with controller):
    With our "fall on backpack" fall control strategy, the humanoid can successfully touch the ground with the backpack under the same push force as above. The assumption is that the design of the backpack is able to better survive an impact than other parts of the robot. The top, middle, and bottom rows show the side, top, and front views, respectively, of the simulation.



  • S.-H Lee and A. Goswami,
    A Momentum-based Balance Controller for Humanoid Robots on Non-level and Non-stationary Ground,
    Journal of Autonomous Robots, Volume 33, Number 4, November 2012.
    (pdf).

    Simulation video:
    Click Here

    Abstract:
    Recent research suggests the importance of controlling rotational dynamics of a humanoid robot in balance maintenance and gait. In this paper, we present a novel balance strategy that controls both linear and angular momentum of the robot. The controller's objective is defined in terms of the desired momenta, allowing intuitive control of the balancing behavior of the robot. By directly determining the ground reaction force (GRF) and the center of pressure (CoP) at each support foot to realize the desired momenta, this strategy can deal with non-level and non-stationary grounds, as well as different frictional properties at each foot-ground contact. When the robot cannot realize the desired values of linear and angular momenta simultaneously, the controller attributes higher priority to linear momentum at the cost of compromising angular momentum. This creates a large rotation of the upper body, reminiscent of the balancing behavior of humans. We develop a computationally efficient method to optimize GRFs and CoPs at individual foot by sequentially solving two small-scale constrained linear least-squares problems. The balance strategy is demonstrated on a simulated humanoid robot under experiments such as recovery from unknown external pushes and balancing on non-level and moving supports.

    Features:


    Overview of Momentum-Based Balance Controller.

    Simulation:

    Figure above:
    Given a forward push, the balance controller controls both linear and angular momentum, and generates a motion comparable to human's balance control behavior. The robot is standing on stationary level platforms.



    Figure above:
    The single-supported robot on stationary level support successfully recovers from a leftward push.



    Figure above:
    The two supports translate forward and backward with the same speed. In order to maintain balance, the robot rotates its trunk in a periodic manner. The red arrows indicate the direction and magnitude of the linear momentum of the robot. Note that the two feet of the robot have different ankle angles to conform to the different slopes of the moving platforms.


    Figure above:
    The robot maintains balance on moving supports. The two foot support surfaces have different inclination angles and out of phase front-back velocities.


  • J. Chiu and A. Goswami,
    Driver Assist for Backing-Up a Vehicle with a Long-Wheelbase Dual-Axle Trailer,
    AVEC 2012, Seoul, Korea, September 2012.
    (pdf).
    Backing up a vehicle and trailer is a tricky task. If you are not careful you may end up in a jackknife situation in which the trailer and vehicle fold on each other. We present a human in the loop control where jackknife is avoided using a trailer with rear steering.

    Abstract:
    Backing-up of articulated vehicles poses a difficult challenge even for experienced drivers. While long wheelbase dual-axle trailers provide a benefit of increased capacity over their single-axle counterparts, backing-up of such systems is especially difficult. We propose a control strategy for such systems, introducing concepts of the hitch control space and no-slip curve derived from no-slip kinematics, allowing backing-up maneuvers to be intuitive to drivers without experience with trailers. Using hitch angle feedback, we show these concepts can be used to stabilize the trailer in back-up motion in the presence of arbitrary driver inputs. The controller is tested in simulation and on a scale model testbed, demonstrating that robust and stable backing-up of such systems can be achieved whilst allowing the driver to maintain full control of the vehicle.


  • T. Koolen, T. de Boer, J. Rebula, A. Goswami and J. Pratt,
    Capturability Based Analysis and Control of Legged Locomotion, Part 1: Application to Three Simple Gait Models,
    International Journal of Robotics Research, Vol. 31 No. 9, August 2012.
    (pdf).


    Abstract:
    This paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability.

    The paper introduces a theoretical framework for assessing N-step capturability. This framework is used to analyze three simple models of legged locomotion. All three models are based on the 3D Linear Inverted Pendulum Model. The first model relies solely on a point foot step location to maintain balance, the second model adds a finite-sized foot, and the third model enables the use of centroidal angular momentum by adding a reaction mass. We analyze how these mechanisms influence N-step capturability, for any N > 0.

    Features:



    Figure above:
    Conceptual view of the state space of a hybrid dynamic system. Several N-step viable-capture basins are shown. The boundary between two N-step viable-capture basins is part of a step surface. The infinity-step viable-capture basin approximates the viability kernel. Several evolutions are shown: a) an evolution starting outside the viability kernel inevitably ends up in the set of failed states; b) the system starts in the 1-step viable-capture basin, takes a step, and comes to a rest at a fixed point inside the set of captured states (i.e. the 0-step viable-capture basin); c) an evolution that eventually converges to a limit cycle; d) an evolution that has the same initial state as c), but ends up in the set of failed states because the input u(.) was different; e) impossible evolution: by definition, it is impossible to enter the viability kernel if the initial state is outside the viability kernel.



    Figure above:
    a) A conceptual representation of the N- step capture regions for a human in a captured state (standing at rest). b) N-step capture regions for a running human. The capture regions have decreased in size and have shifted, as compared to a). c) N-step capture regions for the same state as b), but with sparse footholds (e.g. stepping stones in a pond). The set of failed states has changed, which is re ected in the capture regions.



    Figure above:
    Schematic representations of a 3D-LIPM (Linear Inverted Pendulum Model) with point foot, a 3D-LIPM with finite-sized foot and a 3D-LIPM with finite-sized foot and reaction mass with a non-zero mass moment of inertia tensor.


  • S.-K. Yun and A. Goswami,
    Hardware Experiments of Humanoid Robot Safe Fall using Aldebaran NAO,
    ICRA 2012, St. Paul, MN, May 2012.
    (pdf).

    Simulation video:
    Click Here


    This paper reports successful experimental demonstration of direction-changing fall control strategy of humanoid robots.

    Abstract:
    Although the fall of a humanoid robot is rare in controlled environments, it cannot be avoided in the real world where the robot may physically interact with the environment. Our earlier work introduced the strategy of direction-changing fall, in which the robot attempts to reduce the chance of human injury by changing its default fall direction in real-time and falling in a safer direction. The current paper reports further theoretical developments culminating in a successful hardware implementation of this fall strategy conducted on the Aldebaran NAO robot. This includes new algorithms for humanoid kinematics and Jacobians involving coupled joints and a complete estimation of the body frame attitude using an additional inertial measurement unit. Simulations and experiments are smoothly handled by our platform independent humanoid control software package called Locomote. We report experiment scenarios where we demonstrate the effectiveness of the proposed strategies in changing humanoid fall direction.

    Features:


    Without a fall controller, when a humanoid is pushed from behind (left photo), it topples forward (middle photo) and falls on its face (right photo).



    With a fall control strategy, which in this case is lifting right foot, the humanoid can fall to the right under the same push force as above.



    With an inertia shaping fall controller, the humanoid can fall diagonally, again under the same push force as above.


  • Gabriel Aguirre-Ollinger, J. Edward Colgate, Michael A. Peshkin, and A. Goswami,
    Inertia Compensation Control of a One-Degree-of-Freedom Exoskeleton for Lower-Limb Assistance: Initial Experiments,
    IEEE Transactions on Neural Systems Rehabilitation Engineering, Vol. 20, No. 1, January 2012.
    (pdf).


    Abstract:
    A new method of lower-limb exoskeleton control aimed at improving the agility of leg-swing motion is presented. In the absence of control, an exoskeleton's mechanism usually hinders agility by adding mechanical impedance to the legs. The uncompensated inertia of the exoskeleton will reduce the natural frequency of leg swing, probably leading to lower step frequency during walking as well as increased metabolic energy consumption. The proposed controller emulates inertia compensation by adding a feedback loop consisting of low-pass filtered angular acceleration multiplied by a negative gain. This gain simulates negative inertia in the low-frequency range. The resulting controller combines two assistive effects: increasing the natural frequency of the lower limbs and performing net work per swing cycle. The controller was tested on a statically mounted exoskeleton that assists knee flexion and extension. Subjects performed movement sequences, first unassisted and then using the exoskeleton, in the context of a computer-based task resembling a race. In the exoskeleton's baseline state, the frequency of leg swing and the mean angular velocity were consistently reduced. The addition of inertia compensation enabled subjects to recover their normal frequency and increase their selected angular velocity. The work performed by the exoskeleton was evidenced by catch trials in the protocol.

  • S.-K. Yun and A. Goswami,
    Momentum-Based Reactive Stepping Controller on Level and Non-level Ground for Humanoid Robot Push Recovery,
    IROS 2011, San Francisco, CA, September 2011.
    (pdf).

    Simulation video:
    Click Here

    This paper introduces the General Foot Placement Estimator (GFPE) point. The GFPE point is the point at which a robot should step to, on level or non-level surface, after a push, in order to come to a complete stop with a vertically upright configuration.

    Abstract:
    This paper presents a momentum-based reactive stepping controller for humanoid robot push recovery. By properly regulating combinations of linear and angular momenta, the controller can selectively encourage the robot to recover its balance with or without taking a step. A reference stepping location is computed by modeling the humanoid as a passive rimless wheel with two spokes such that stepping on the location leads to a complete stop of the wheel at the vertically upright position. In contrast to most reference points for stepping based on pendulum models such as the capture point, our reference point exists on both level and non-level grounds. Moreover, in contrast with continuously evolving step locations, our step location is stationary. The computation of the location of the reference point also generates the duration of step which can be used for designing a stepping trajectory. Momentum-based stepping for push recovery is implemented in simulations of a full size humanoid on 3D non-level ground.

    Features:


    Humanoid stepping on a 11.5 degree uphill under various push forces.



    Humanoid stepping on a 6 degree downhill under various push forces.


List of co-authors (Advisors, mentors, students, interns)

Over the years I have had the priviledge to work with a number of gifted researchers. The following is an alphabetical list of people with whom I have had publications in the last 3 years (the full list is here).
Free data and matlab code for human gait cyclogram analysis, click here.
Free data and matlab code for dynamic analysis of passive Compass Gait robot, click here.

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Page(s) last updated November 3, 2013