Space-time functional gradient optimization for motion planning

Functional gradient algorithms (e.g. CHOMP) have recently shown great promise for producing locally optimal motion for complex many degree-of-freedom robots. A key limitation of such algorithms is the difficulty in incorporating constraints and cost functions that explicitly depend on time. We present T-CHOMP, a functional gradient algorithm that overcomes this limitation by directly optimizing in space-time. We outline a framework for joint space-time optimization, derive an efficient trajectory-wide update for maintaining time monotonicity, and demonstrate the significance of T-CHOMP over CHOMP in several scenarios. By manipulating time, T-CHOMP produces lower-cost trajectories leading to behavior that is meaningfully different from CHOMP.

[1]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.

[2]  David Q. Mayne,et al.  Differential dynamic programming , 1972, The Mathematical Gazette.

[3]  John Halas,et al.  Timing for Animation , 1981 .

[4]  J. Hollerbach.  Dynamic Scaling of Manipulator Trajectories , 1983, 1983 American Control Conference.

[5]  M. Jeannerod.  The timing of natural prehension movements. , 1984, Journal of motor behavior.

[6]  J. Bobrow,et al.  Time-Optimal Control of Robotic Manipulators Along Specified Paths , 1985 .

[7]  Andrew P. Witkin,et al.  Spacetime constraints , 1988, SIGGRAPH.

[8]  Bruce Randall Donald,et al.  On the complexity of kinodynamic planning , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[9]  Oussama Khatib,et al.  Real-Time Obstacle Avoidance for Manipulators and Mobile Robots , 1985, Autonomous Robot Vehicles.

[10]  Steven Dubowsky,et al.  On computing the global time-optimal motions of robotic manipulators in the presence of obstacles , 1991, IEEE Trans. Robotics Autom..

[11]  Michael F. Cohen,et al.  Interactive spacetime control for animation , 1992, SIGGRAPH.

[12]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[13]  Oussama Khatib,et al.  Elastic bands: connecting path planning and control , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[14]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[15]  Zoran Popovic,et al.  Motion warping , 1995, SIGGRAPH.

[16]  Michael Gleicher,et al.  Retargetting motion to new characters , 1998, SIGGRAPH.

[17]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[18]  Zoran Popovic,et al.  Physically based motion transformation , 1999, SIGGRAPH.

[19]  Steven M. Seitz,et al.  Interactive manipulation of rigid body simulations , 2000, SIGGRAPH.

[20]  E. Todorov,et al.  A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[21]  Siddhartha S. Srinivasa,et al.  Physics-based motion retiming , 2006, SCA '06.

[22]  Anind K. Dey,et al.  Maximum Entropy Inverse Reinforcement Learning , 2008, AAAI.

[23]  Alois Knoll,et al.  Human-robot interaction in handing-over tasks , 2008, RO-MAN 2008 - The 17th IEEE International Symposium on Robot and Human Interactive Communication.

[24]  James J. Kuffner,et al.  OpenRAVE: A Planning Architecture for Autonomous Robotics , 2008 .

[25]  Siddhartha S. Srinivasa,et al.  CHOMP: Gradient optimization techniques for efficient motion planning , 2009, 2009 IEEE International Conference on Robotics and Automation.

[26]  Marc Toussaint,et al.  Robot trajectory optimization using approximate inference , 2009, ICML '09.

[27]  Stefan Schaal,et al.  Reinforcement learning of motor skills in high dimensions: A path integral approach , 2010, 2010 IEEE International Conference on Robotics and Automation.

[28]  Marc Toussaint,et al.  An Approximate Inference Approach to Temporal Optimization in Optimal Control , 2010, NIPS.

[29]  U. Castiello,et al.  Toward You , 2010 .

[30]  Stefan Schaal,et al.  STOMP: Stochastic trajectory optimization for motion planning , 2011, 2011 IEEE International Conference on Robotics and Automation.

[31]  Pieter Abbeel,et al.  LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information , 2010, Int. J. Robotics Res..

[32]  Siddhartha S. Srinivasa,et al.  Human preferences for robot-human hand-over configurations , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[33]  Siddhartha S. Srinivasa,et al.  Manipulation planning with goal sets using constrained trajectory optimization , 2011, 2011 IEEE International Conference on Robotics and Automation.

[34]  Andrea Lockerd Thomaz,et al.  Spatiotemporal correspondence as a metric for human-like robot motion , 2011, 2011 6th ACM/IEEE International Conference on Human-Robot Interaction (HRI).

[35]  P. Abbeel,et al.  LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information , 2011 .

[36]  Chonhyon Park,et al.  ITOMP: Incremental Trajectory Optimization for Real-Time Replanning in Dynamic Environments , 2012, ICAPS.

[37]  Pieter Abbeel,et al.  Finding Locally Optimal, Collision-Free Trajectories with Sequential Convex Optimization , 2013, Robotics: Science and Systems.

[38]  Siddhartha S. Srinivasa,et al.  CHOMP: Covariant Hamiltonian optimization for motion planning , 2013, Int. J. Robotics Res..