Towards constrained motion planning of mobile manipulators

This paper addresses a constrained motion planning problem for mobile manipulators. The constraints are included into the system model by means of a sort of penalty function, and then processed in accordance with the endogenous configuration space approach. Main novelty of this paper lies in deriving a constrained Jacobian motion planning algorithm with the following features: inequality constraints are included into an extended kinematics model using a smooth approximation of the plus function, the model is then regularized against singularities, and the resulting imbalance in error equations is handled as a perturbation of an exponentially stable linear dynamic system. The operation of the constrained motion planning algorithm is illustrated by a motion planning problem of a mobile manipulator with bounds imposed on a platform variable. Performance of the algorithm is tested by computer simulations.

[1]  Héctor J. Sussmann,et al.  Line-Integral Estimates and Motion Planning Using the Continuation Method , 1998 .

[2]  John T. Wen,et al.  A path space approach to nonholonomic motion planning in the presence of obstacles , 1997, IEEE Trans. Robotics Autom..

[3]  Olvi L. Mangasarian,et al.  Smoothing methods for convex inequalities and linear complementarity problems , 1995, Math. Program..

[4]  Krzysztof Tchoń,et al.  Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms , 2003 .

[5]  Krzysztof Tchon.  Optimal Extended Jacobian Inverse Kinematics Algorithms for Robotic Manipulators , 2008, IEEE Transactions on Robotics.

[6]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[7]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[8]  Charles A. Klein,et al.  A new formulation of the extended Jacobian method and its use in mapping algorithmic singularities for kinematically redundant manipulators , 1995, IEEE Trans. Robotics Autom..

[9]  Eduardo Sontag.  Control of systems without drift via generic loops , 1995, IEEE Trans. Autom. Control..

[10]  Stefano Chiaverini,et al.  Singularity-robust task-priority redundancy resolution for real-time kinematic control of robot manipulators , 1997, IEEE Trans. Robotics Autom..

[11]  J. Jakubiak,et al.  On Predictive Approach to Inverse Kinematics of Mobile Manipulators , 2007, 2007 IEEE International Conference on Control and Automation.

[12]  John T. Wen,et al.  Kinematic path planning for robots with holonomic and nonholonomic constraints , 1998 .

[13]  L. Biegler,et al.  Nonlinear Programming Strategies for State Estimation and Model Predictive Control , 2009 .

[14]  A. A. Maciejewski,et al.  Repeatable generalized inverse control strategies for kinematically redundant manipulators , 1993, IEEE Trans. Autom. Control..

[15]  Hans Joachim Ferreau,et al.  Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation , 2009 .

[16]  J. Wen,et al.  Nonlinear Model Predictive Control for the Swing-Up of a Rotary Inverted Pendulum , 2004 .

[17]  Janusz Jakubiak,et al.  Extended Jacobian inverse kinematics algorithms for mobile manipulators , 2002, J. Field Robotics.

[18]  Victor M. Zavala,et al.  Fast implementations and rigorous models: Can both be accommodated in NMPC? , 2008 .

[19]  J. Jakubiak,et al.  Extended jacobian motion planning algorithm for mobile manipulators , 2003 .