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A Quadratic Programming Approach to Quasi-Static Whole-Body Manipulation

Shankar, Krishna and Burdick, Joel W. and Hudson, Nicolas H (2015) A Quadratic Programming Approach to Quasi-Static Whole-Body Manipulation. In: Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics. No.107. Springer , Cham, pp. 553-570. ISBN 978-3-319-16594-3.

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This paper introduces a local motion planning method for robotic systems with manipulating limbs, moving bases (legged or wheeled), and stance stability constraints arising from the presence of gravity. We formulate the problem of selecting local motions as a linearly constrained quadratic program (QP), that can be solved efficiently. The solution to this QP is a tuple of locally optimal joint velocities. By using these velocities to step towards a goal, both a path and an inverse-kinematic solution to the goal are obtained. This formulation can be used directly for real-time control, or as a local motion planner to connect waypoints. This method is particularly useful for high-degree-of-freedom mobile robotic systems, as the QP solution scales well with the number of joints. We also show how a number of practically important geometric constraints (collision avoidance, mechanism self-collision avoidance, gaze direction, etc.) can be readily incorporated into either the constraint or objective parts of the formulation. Additionally, motion of the base, a particular joint, or a particular link can be encouraged/discouraged as desired. We summarize the important kinematic variables of the formulation, including the stance Jacobian, the reach Jacobian, and a center of mass Jacobian. The method is easily extended to provide sparse solutions, where the fewest number of joints are moved, by iteration using Tibshirani’s method to accommodate an l_1 regularizer. The approach is validated and demonstrated on SURROGATE, a mobile robot with a TALON base, a 7 DOF serial-revolute torso, and two 7 DOF modular arms developed at JPL/Caltech.

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Additional Information:© 2015 Springer International Publishing Switzerland.
Series Name:Springer Tracts in Advanced Robotics
Issue or Number:107
Record Number:CaltechAUTHORS:20141028-073430685
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50894
Deposited By: Krishna Shankar
Deposited On:28 Oct 2014 17:20
Last Modified:03 Oct 2019 07:27

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