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Mistry M.,Disney Research Pittsburgh | Righetti L.,University of Southern California
Robotics: Science and Systems | Year: 2012

The operational space formulation (Khatib, 1987), applied to rigid-body manipulators, describes how to decouple task-space and null space dynamics, and write control equations that correspond only to forces at the end-effector or, alternatively, only to motion within the null space. We would like to apply this useful theory to modern humanoids and other legged systems, for manipulation or similar tasks, however these systems present additional challenges due to their underactuated floating bases and contact states that can dynamically change. In recent work, Sentis et al. derived controllers for such systems by implementing a task Jacobian projected into a space consistent with the supporting constraints and underactuation (the so called support consistent reduced Jacobian). Here, we take a new approach to derive operational space controllers for constrained underactuated systems, by first considering the operational space dynamics within projected inverse-dynamics (Aghili, 2005), and subsequently resolving underactuation through the addition of dynamically consistent control torques. Doing so results in a simplified control solution compared with previous results, and importantly yields several new insights into the underlying problem of operational space control in constrained environments: 1) Underactuated systems, such as humanoid robots, cannot in general completely decouple task and null space dynamics. However, 2) there may exist an infinite number of control solutions to realize desired task-space dynamics, and 3) these solutions involve the addition of dynamically consistent null space motion or constraint forces (or combinations of both). In light of these findings, we present several possible control solutions, with varying optimization criteria, and highlight some of their practical consequences. Source


Bhounsule P.A.,Disney Research Pittsburgh
Robotica | Year: 2015

In this paper, we present a theoretical study on the control of a compass gait walker using energy regulation between steps. We use a return map to relate the mid-stance robot kinetic energy between steps with two control inputs, namely, foot placement and ankle push-off. We show that by regulating robot kinetic energy between steps using the two control inputs, we are able to (1) generate a wide range of walking speeds and stride lengths, including average human walking; (2) cancel the effect of external disturbance fully in a single step (dead-beat control); and (3) switch from one periodic gait to another in a single step. We hope that insights from this control methodology can help develop robust controllers for practical bipedal robots. Copyright © Cambridge University Press 2014. Source


Righetti L.,University of Southern California | Buchli J.,Italian Institute of Technology | Mistry M.,Disney Research Pittsburgh | Schaal S.,University of Southern California
Proceedings - IEEE International Conference on Robotics and Automation | Year: 2011

Inverse dynamics controllers and operational space controllers have proved to be very efficient for compliant control of fully actuated robots such as fixed base manipulators. However legged robots such as humanoids are inherently different as they are underactuated and subject to switching external contact constraints. Recently several methods have been proposed to create inverse dynamics controllers and operational space controllers for these robots. In an attempt to compare these different approaches, we develop a general framework for inverse dynamics control and show that these methods lead to very similar controllers. We are then able to greatly simplify recent whole-body controllers based on operational space approaches using kinematic projections, bringing them closer to efficient practical implementations. We also generalize these controllers such that they can be optimal under an arbitrary quadratic cost in the commands. © 2011 IEEE. Source


Bhounsule P.A.,Disney Research Pittsburgh | Bhounsule P.A.,University of Texas at San Antonio
IEEE Transactions on Robotics | Year: 2014

We show that the simplest slope walker can walk over wide combinations of step lengths and step velocities at a given ramp slope by proper choice of foot placement. We are able to find walking solutions up to slope of 15.42 °, beyond which, the ground reaction force on the stance leg goes to zero, implying a flight phase. We also show that the simplest walker can walk at human-sized step length and step velocity at a slope of 6.62 °. The central idea behind control using foot placement is to balance the potential energy gained during descent with the energy lost during collision at foot-strike. Finally, we give some suggestions on how the ideas from foot placement control and energy balance can be extended to realize walking motions on practical legged systems. © 2014 IEEE. Source


Akhter I.,Disney Research Pittsburgh | Simon T.,Carnegie Mellon University | Khan S.,Lahore University of Management Sciences | Matthews I.,Carnegie Mellon University | Sheikh Y.,Carnegie Mellon University
ACM Transactions on Graphics | Year: 2012

A variety of dynamic objects, such as faces, bodies, and cloth, are represented in computer graphics as a collection of moving spatial landmarks. Spatiotemporal data is inherent in a number of graphics applications including animation, simulation, and object and camera tracking. The principal modes of variation in the spatial geometry of objects are typically modeled using dimensionality reduction techniques, while concurrently, trajectory representations like splines and autoregressive models are widely used to exploit the temporal regularity of deformation. In this article, we present the bilinear spatiotemporal basis as a model that simultaneously exploits spatial and temporal regularity while maintaining the ability to generalize well to new sequences. This factorization allows the use of analytical, predefined functions to represent temporal variation (e.g., B-Splines or the Discrete Cosine Transform) resulting in efficient model representation and estimation. The model can be interpreted as representing the data as a linear combination of spatiotemporal sequences consisting of shape modes oscillating over time at key frequencies. We apply the bilinear model to natural spatiotemporal phenomena, including face, body, and cloth motion data, and compare it in terms of compaction, generalization ability, predictive precision, and efficiency to existing models. We demonstrate the application of the model to a number of graphics tasks including labeling, gap-filling, denoising, and motion touch-up. © 2012 ACM. Source

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