Footstep planning on uneven terrain with mixed-integer convex optimization

We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1].

[1]  Olle Seger,et al.  Generalized and Separable Sobel Operators , 1990 .

[2]  Herbert Freeman,et al.  Machine Vision for Three-Dimensional Scenes , 1990 .

[3]  Masayuki Inaba,et al.  Footstep planning among obstacles for biped robots , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[4]  Jonathan P. How,et al.  COORDINATION AND CONTROL OF MULTIPLE UAVs , 2002 .

[5]  J. Chestnutt,et al.  Planning Biped Navigation Strategies in Complex Environments , 2003 .

[6]  Masayuki Inaba,et al.  Online footstep planning for humanoid robots , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[7]  Timothy Bretl,et al.  Multi-Step Motion Planning for Free-Climbing Robots , 2004, WAFR.

[8]  Takeo Kanade,et al.  Vision-guided humanoid footstep planning for dynamic environments , 2005, 5th IEEE-RAS International Conference on Humanoid Robots, 2005..

[9]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[10]  Satoshi Kagami,et al.  An adaptive action model for legged navigation planning , 2007, 2007 7th IEEE-RAS International Conference on Humanoid Robots.

[11]  Andrei Herdt,et al.  Online Walking Motion Generation with Automatic Footstep Placement , 2010, Adv. Robotics.

[12]  Ian R. Manchester,et al.  Bounding on rough terrain with the LittleDog robot , 2011, Int. J. Robotics Res..

[13]  Jerry E. Pratt,et al.  Comprehensive summary of the Institute for Human and Machine Cognition’s experience with LittleDog , 2011, Int. J. Robotics Res..

[14]  Java Binding,et al.  GNU Linear Programming Kit , 2011 .

[15]  Olivier Stasse,et al.  Real-time replanning using 3D environment for humanoid robot , 2011, 2011 11th IEEE-RAS International Conference on Humanoid Robots.

[16]  Anna Gorbenko,et al.  Footstep Planning for Humanoid Robots , 2012 .

[17]  Maren Bennewitz,et al.  Anytime search-based footstep planning with suboptimality bounds , 2012, 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012).

[18]  Robin Deits,et al.  Computing Large Convex Regions of Obstacle-Free Space Through Semidefinite Programming , 2014, WAFR.

[19]  Scott Kuindersma,et al.  An Architecture for Online Affordance‐based Perception and Whole‐body Planning , 2015, J. Field Robotics.