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22
Capture point: A step toward humanoid push recovery
 in 6th IEEERAS International Conference on Humanoid Robots
, 2006
"... 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 ..."
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Cited by 67 (5 self)
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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. I.
Momentum control for balance
 ACM TRANS. ON GRAPHICS
, 2009
"... We demonstrate a realtime simulation system capable of automatically balancing a standing character, while at the same time tracking a reference motion and responding to external perturbations. The system is general to nonhuman morphologies and results in natural balancing motions employing the en ..."
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Cited by 52 (3 self)
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We demonstrate a realtime simulation system capable of automatically balancing a standing character, while at the same time tracking a reference motion and responding to external perturbations. The system is general to nonhuman morphologies and results in natural balancing motions employing the entire body (for example, windmilling). Our novel balance routine seeks to control the linear and angular momenta of the character. We demonstrate how momentum is related to the center of mass and center of pressure of the character and derive control rules to change these centers for balance. The desired momentum changes are reconciled with the objective of tracking the reference motion through an optimization routine which produces target joint accelerations. A hybrid inverse/forward dynamics algorithm determines joint torques based on these joint accelerations and the ground reaction forces. Finally, the joint torques are applied to the freestanding character simulation. We demonstrate results for following both motion capture and keyframe data as well as both human and nonhuman morphologies in presence of a variety of conditions and disturbances.
Interactive Simulation of Stylized Human Locomotion
 ACM TRANSACTIONS ON GRAPHICS
"... Animating natural human motion in dynamic environments is difficult because of complex geometric and physical interactions. Simulation provides an automatic solution to parts of this problem, but it needs control systems to produce lifelike motions. This paper describes the systematic computation of ..."
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Cited by 42 (5 self)
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Animating natural human motion in dynamic environments is difficult because of complex geometric and physical interactions. Simulation provides an automatic solution to parts of this problem, but it needs control systems to produce lifelike motions. This paper describes the systematic computation of controllers that can reproduce a range of locomotion styles in interactive simulations. Given a reference motion that describes the desired style, a derived control system can reproduce that style in simulation and in new environments. Because it produces highquality motions that are both geometrically and physically consistent with simulated surroundings, interactive animation systems could begin to use this approach along with more established kinematic methods.
Standing Balance Control Using a Trajectory Library
"... Abstract — This paper presents a standing balance controller. We employ a library of optimal trajectories and the neighboring optimal control method to generate local approximations to the optimal control. We take advantage of a parametric nonlinear optimization method, SNOPT, to generate initial tr ..."
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Cited by 22 (6 self)
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Abstract — This paper presents a standing balance controller. We employ a library of optimal trajectories and the neighboring optimal control method to generate local approximations to the optimal control. We take advantage of a parametric nonlinear optimization method, SNOPT, to generate initial trajectories and then use Differential Dynamic Programming (DDP) to further refine them and get their neighboring optimal control. A library generation method is proposed, which keeps the trajectory library to a reasonable size. We compare the proposed controller with an optimal controller and an LQR based gain scheduling controller using the same optimization criterion. Simulation results demonstrate the performance of the proposed method. I.
VelocityBased Stability Margins for Fast Bipedal Walking
 In Fast Motions in Biomechanics and Robotics
, 2006
"... We present velocitybased stability margins for fast bipedal walking that are sufficient conditions for stability, allow comparison between different walking algorithms, are measurable and computable, and are meaningful. While not completely necessary conditions, they are tighter necessary condition ..."
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Cited by 21 (0 self)
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We present velocitybased stability margins for fast bipedal walking that are sufficient conditions for stability, allow comparison between different walking algorithms, are measurable and computable, and are meaningful. While not completely necessary conditions, they are tighter necessary conditions than several previously proposed stability margins. The stability margins we present take into consideration a biped’s Center of Mass position and velocity, the reachable region of its swing leg, the time required to swing its swing leg, and the amount of internal angular momentum available for capturing balance. They predict the opportunity for the biped to place its swing leg in such a way that it can continue walking without falling down. We present methods for estimating these stability margins by using simple models of walking such as an inverted pendulum model and the Linear Inverted Pendulum model. We show that by considering the Center of Mass location with respect to the Center of Pressure on the foot, these estimates are easily computable. Finally, we show through simulation experiments on a 12 degreeoffreedom distributedmass lowerbody biped that these estimates are useful for analyzing and controlling bipedal walking. 2
Realtime physicsbased 3D biped character animation using an inverted pendulum model
 IEEE transactions on visualization and computer graphics
"... Abstract—We present a physicsbased approach to generate 3D biped character animation that can react to dynamical environments in real time. Our approach utilizes an inverted pendulum model to online adjust the desired motion trajectory from the input motion capture data. This online adjustment prod ..."
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Cited by 20 (4 self)
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Abstract—We present a physicsbased approach to generate 3D biped character animation that can react to dynamical environments in real time. Our approach utilizes an inverted pendulum model to online adjust the desired motion trajectory from the input motion capture data. This online adjustment produces a physically plausible motion trajectory adapted to dynamic environments, which is then used as the desired motion for the motion controllers to track in dynamics simulation. Rather than using ProportionalDerivative controllers whose parameters usually cannot be easily set, our motion tracking adopts a velocitydriven method which computes joint torques based on the desired joint angular velocities. Physically correct fullbody motion of the 3D character is computed in dynamics simulation using the computed torques and dynamical model of the character. Our experiments demonstrate that tracking motion capture data with realtime response animation can be achieved easily. In addition, physically plausible motion style editing, automatic motion transition, and motion adaptation to different limb sizes can also be generated without difficulty. Index Terms—3D human motion, physicsbased simulation, biped walk and balance, motion capture data. Ç 1
Reaction mass pendulum (RMP): An explicit model for centroidal angular momentum of humanoid robots
 in Proceedings of the IEEE International Conference on Robotics & Automation
, 2007
"... 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 ..."
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Cited by 13 (3 self)
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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 betterknown 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. I.
Velocity Based Stability Margins for Fast Bipedal Walking
 In "Fast Motions in Biomechanics and Robots
, 2005
"... We present velocity based stability margins for fast bipedal walking that are sufficient conditions for stability, allow comparison between different walking algorithms, are measurable and computable, and are meaningful. While not completely necessary conditions, they are tighter necessary conditio ..."
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Cited by 13 (5 self)
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We present velocity based stability margins for fast bipedal walking that are sufficient conditions for stability, allow comparison between different walking algorithms, are measurable and computable, and are meaningful. While not completely necessary conditions, they are tighter necessary conditions than several previously proposed stability margins. The stability margins we present take into consideration a biped’s Center of Mass position and velocity, the reachable region of its swing leg, the time required to swing its swing leg, and the amount of internal angular momentum available for capturing balance. They predict the opportunity for the biped to place its swing leg in such a way that it can continue walking without falling down. We present methods for estimating these stability margins by using simple models of walking such as an inverted pendulum model and the Linear Inverted Pendulum model. We show that by considering the Center of Mass location with respect to the Center of Pressure on the foot, these estimates are easily computable. Finally, we show through simulation experiments on a 12 degreeoffreedom distributedmass lowerbody biped that these estimates are useful for analyzing and controlling bipedal walking. 2
Online Learning of a Full Body Push Recovery Controller for Omnidirectional Walking
"... Abstract — Bipedal humanoid robots are inherently unstable to external perturbations, especially when they are walking on uneven terrain in the presence of unforeseen collisions. In this paper, we present a push recovery controller for positioncontrolled humanoid robots which is tightly integrated ..."
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Cited by 9 (4 self)
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Abstract — Bipedal humanoid robots are inherently unstable to external perturbations, especially when they are walking on uneven terrain in the presence of unforeseen collisions. In this paper, we present a push recovery controller for positioncontrolled humanoid robots which is tightly integrated with an omnidirectional walk controller. The high level push recovery controller learns to integrate three biomechanically motivated push recovery strategies with a zero moment point based omnidirectional walk controller. Reinforcement learning is used to map the robot walking state, consisting of foot configuration and onboard sensory information, to the best combination of the three biomechanical responses needed to reject external perturbations. Experimental results show how this online method can stabilize an inexpensive, commerciallyavailable DARwinOP small humanoid robot.
A.: Centroidal Momentum Matrix of a humanoid robot: Structure and Properties
 In: IEEE/RSJ Intl Conf on Intelligent Robots and Systems (2008
"... 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 func ..."
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Cited by 8 (2 self)
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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 wellknown jointspace inertia matrix. We present a Transformation Diagram that graphically captures the interrelationships 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. Index Terms—momentum matrix, inertia matrix, angular momentum, linear momentum, matrix properties, centroidal momentum ellipsoid. I.