Geometry-aware Manipulability Tracking and Transfer

Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or apply a specific force. In this context, this paper presents a novel manipulability transfer framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.

[1]  Satoshi Kagami,et al.  Manipulability optimization for trajectory generation , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[2]  Michael N. Mistry,et al.  Dynamic manipulability of the center of mass: A tool to study, analyse and measure physical ability of robots , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[3]  Tsuneo Yoshikawa,et al.  Dynamic Manipulability of Robot Manipulators , 1985 .

[4]  Sylvain Calinon,et al.  Gaussian mixture regression on symmetric positive definite matrices manifolds: Application to wrist motion estimation with sEMG , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[5]  Jun-Ho Oh,et al.  Humanoid Posture Selection for Reaching Motion and a Cooperative Balancing Controller , 2016, J. Intell. Robotic Syst..

[6]  S. Chiu,et al.  Control of redundant manipulators for task compatibility , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[7]  Bin Yao,et al.  Feasible Center of Mass Dynamic Manipulability of humanoid robots , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[8]  Carme Torras,et al.  Learning Physical Collaborative Robot Behaviors From Human Demonstrations , 2016, IEEE Transactions on Robotics.

[9]  Jun Nakanishi,et al.  Inverse kinematics with floating base and constraints for full body humanoid robot control , 2008, Humanoids 2008 - 8th IEEE-RAS International Conference on Humanoid Robots.

[10]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[11]  Francesc Moreno-Noguer,et al.  3D Human Pose Tracking Priors using Geodesic Mixture Models , 2017, International Journal of Computer Vision.

[12]  P. Cisek,et al.  The influence of predicted arm biomechanics on decision making. , 2011, Journal of neurophysiology.

[13]  Xavier Pennec,et al.  A Riemannian Framework for Tensor Computing , 2005, International Journal of Computer Vision.

[14]  Sukhan Lee,et al.  Dual redundant arm configuration optimization with task-oriented dual arm manipulability , 1989, IEEE Trans. Robotics Autom..

[15]  Giulio Sandini,et al.  Manipulability analysis , 2012, 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012).

[16]  J. Y. S. Luh,et al.  Constrained Relations between Two Coordinated Industrial Robots for Motion Control , 1987 .

[17]  Antonio Bicchi,et al.  On the manipulability ellipsoids of underactuated robotic hands with compliance , 2012, Robotics Auton. Syst..

[18]  Diego Colon,et al.  Some properties of the Riemannian distance function and the position vector X, with applications to the construction of Lyapunov functions , 2010, 49th IEEE Conference on Decision and Control (CDC).

[19]  Bruno Siciliano,et al.  Global task space manipulability ellipsoids for multiple-arm systems , 1991, IEEE Trans. Robotics Autom..

[20]  Søren Hauberg,et al.  Model Transport: Towards Scalable Transfer Learning on Manifolds , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[21]  B. Siciliano,et al.  Reformulation of dynamic manipulability ellipsoid for robotic manipulators , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[22]  Suvrit Sra,et al.  A new metric on the manifold of kernel matrices with application to matrix geometric means , 2012, NIPS.

[23]  F. Park,et al.  Manipulability of Closed Kinematic Chains , 1998 .

[24]  Alois Knoll,et al.  Task level robot programming using prioritized non-linear inequality constraints , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[25]  Jörn Malzahn,et al.  Development of a human size and strength compliant bi-manual platform for realistic heavy manipulation tasks , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[26]  P. Morasso.  Spatial control of arm movements , 2004, Experimental Brain Research.

[27]  Darwin G. Caldwell,et al.  Learning manipulability ellipsoids for task compatibility in robot manipulation , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[28]  Tsuneo Yoshikawa,et al.  Manipulability of Robotic Mechanisms , 1985 .

[29]  Frank C. Park,et al.  Optimal Robot Design and Differential Geometry , 1995 .

[30]  Darwin G. Caldwell,et al.  Geometry-aware Tracking of Manipulability Ellipsoids , 2018, Robotics: Science and Systems.

[31]  Pasquale Chiacchio.  Exploiting Redundancy in Minimum-Time Path Following Robot Control , 1990, 1990 American Control Conference.

[32]  Gijs Dubbelman,et al.  Intrinsic statistical techniques for robust pose estimation , 2011 .

[33]  Suvrit Sra,et al.  Conic Geometric Optimization on the Manifold of Positive Definite Matrices , 2013, SIAM J. Optim..

[34]  Darwin G. Caldwell,et al.  An Approach for Imitation Learning on Riemannian Manifolds , 2017, IEEE Robotics and Automation Letters.

[35]  Jihong Lee.  A study on the manipulability measures for robot manipulators , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[36]  Michael I. Jordan,et al.  Obstacle Avoidance and a Perturbation Sensitivity Model for Motor Planning , 1997, The Journal of Neuroscience.

[37]  Marc Toussaint,et al.  Understanding the geometry of workspace obstacles in Motion Optimization , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[38]  Peter J. Basser,et al.  Spectral decomposition of a 4th-order covariance tensor: Applications to diffusion tensor MRI , 2007, Signal Process..

[39]  Natalia Dounskaia,et al.  Preferred directions of arm movements are independent of visual perception of spatial directions , 2013, Experimental Brain Research.