Optimization-based locomotion planning, estimation, and control design for the atlas humanoid robot

This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc.

[1]  Nicholas Rotella,et al.  State estimation for a humanoid robot , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[2]  Victor B. Zordan,et al.  Momentum control for balance , 2009, SIGGRAPH 2009.

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

[4]  Alexander Herzog,et al.  Momentum-based Balance Control for Torque-controlled Humanoids , 2013, ArXiv.

[5]  J. Bortz.  A New Mathematical Formulation for Strapdown Inertial Navigation , 1971, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Twan Koolen,et al.  Team IHMC's Lessons Learned from the DARPA Robotics Challenge Trials , 2015, J. Field Robotics.

[7]  Nancy M. Amato,et al.  Approximate convex decomposition of polygons , 2004, SCG '04.

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

[9]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

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

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

[12]  Aaron D. Ames,et al.  First steps toward underactuated human-inspired bipedal robotic walking , 2012, 2012 IEEE International Conference on Robotics and Automation.

[13]  Shuuji Kajita,et al.  A pattern generator of humanoid robots walking on a rough terrain using a handrail , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[14]  Wolfram Burgard,et al.  OctoMap : A Probabilistic , Flexible , and Compact 3 D Map Representation for Robotic Systems , 2010 .

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

[16]  Florent Lamiraux,et al.  Dynamic walking and whole-body motion planning for humanoid robots: an integrated approach , 2013, Int. J. Robotics Res..

[17]  Weiwei Huang,et al.  Decoupled state estimation for humanoids using full-body dynamics , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[18]  Aaron D. Ames,et al.  Human-inspired control of bipedal robots via control lyapunov functions and quadratic programs , 2013, HSCC '13.

[19]  Robin Deits,et al.  Footstep planning on uneven terrain with mixed-integer convex optimization , 2014, 2014 IEEE-RAS International Conference on Humanoid Robots.

[20]  Taku Komura,et al.  The dynamic postural adjustment with the quadratic programming method , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[21]  Roland Siegwart,et al.  State Estimation for Legged Robots - Consistent Fusion of Leg Kinematics and IMU , 2012, Robotics: Science and Systems.

[22]  Aaron D. Ames,et al.  Control lyapunov functions and hybrid zero dynamics , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[23]  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).

[24]  Nancy S. Pollard,et al.  Animation of Humanlike Characters: Dynamic Motion Filtering with a Physically Plausible Contact Model , 2001 .

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

[26]  Ian R. Manchester,et al.  Regions of Attraction for Hybrid Limit Cycles of Walking Robots , 2010, ArXiv.

[27]  Nicholas Roy,et al.  State estimation for aggressive flight in GPS-denied environments using onboard sensing , 2012, 2012 IEEE International Conference on Robotics and Automation.

[28]  David E. Orin,et al.  Centroidal Momentum Matrix of a humanoid robot: Structure and properties , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[29]  Seth J. Teller,et al.  Drift-free humanoid state estimation fusing kinematic, inertial and LIDAR sensing , 2014, 2014 IEEE-RAS International Conference on Humanoid Robots.

[30]  Alain Micaelli,et al.  Dynamic balance control of humanoids for multiple grasps and non coplanar frictional contacts , 2007, 2007 7th IEEE-RAS International Conference on Humanoid Robots.

[31]  Olivier Stasse,et al.  Real-time 3D SLAM for Humanoid Robot considering Pattern Generator Information , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[33]  Andrzej Lingas,et al.  The Power of Non-Rectilinear Holes , 1982, ICALP.

[34]  Johannes Garimort,et al.  Humanoid navigation with dynamic footstep plans , 2011, 2011 IEEE International Conference on Robotics and Automation.

[35]  Nicolas Mansard,et al.  Generic dynamic motion generation with multiple unilateral constraints , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[36]  Wolfram Burgard,et al.  Monte Carlo localization for mobile robots , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[37]  Alexander Herzog,et al.  Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics , 2013, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[38]  Weiwei Huang,et al.  3D walking based on online optimization , 2013, 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids).

[39]  Robin Deits,et al.  Efficient mixed-integer planning for UAVs in cluttered environments , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[40]  Satoshi Kagami,et al.  Autonomous Navigation of a Humanoid Robot Over Unknown Rough Terrain , 2011, ISRR.

[41]  Russ Tedrake,et al.  Whole-body motion planning with centroidal dynamics and full kinematics , 2014, 2014 IEEE-RAS International Conference on Humanoid Robots.

[42]  Russ Tedrake,et al.  A direct method for trajectory optimization of rigid bodies through contact , 2014, Int. J. Robotics Res..

[43]  Benjamin J. Stephens.  State estimation for force-controlled humanoid balance using simple models in the presence of modeling error , 2011, 2011 IEEE International Conference on Robotics and Automation.

[44]  Kazuhito Yokoi,et al.  Whole-Body Motion Generation Integrating Operator's Intention and Robot's Autonomy in Controlling Humanoid Robots , 2007, IEEE Transactions on Robotics.

[45]  Katja D. Mombaur,et al.  Using optimization to create self-stable human-like running , 2009, Robotica.

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

[47]  Stephen P. Boyd,et al.  Fast Evaluation of Quadratic Control-Lyapunov Policy , 2011, IEEE Transactions on Control Systems Technology.

[48]  Twan Koolen,et al.  Summary of Team IHMC's virtual robotics challenge entry , 2013, 2013 13th IEEE-RAS International Conference on Humanoid Robots (Humanoids).

[49]  Sung-Hee Lee,et al.  A momentum-based balance controller for humanoid robots on non-level and non-stationary ground , 2012, Auton. Robots.

[50]  Maren Bennewitz,et al.  Humanoid robot localization in complex indoor environments , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

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

[52]  L. Biegler,et al.  Active set vs. interior point strategies for model predictive control , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[53]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[54]  Kazuhito Yokoi,et al.  Resolved momentum control: humanoid motion planning based on the linear and angular momentum , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[55]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

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

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

[58]  François Keith,et al.  Dynamic Whole-Body Motion Generation Under Rigid Contacts and Other Unilateral Constraints , 2013, IEEE Transactions on Robotics.

[59]  Scott Kuindersma,et al.  An efficiently solvable quadratic program for stabilizing dynamic locomotion , 2013, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[60]  Jovan Popovic,et al.  Multiobjective control with frictional contacts , 2007, SCA '07.

[61]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[62]  H. J. Ferreau,et al.  An online active set strategy to overcome the limitations of explicit MPC , 2008 .