Synthesis of dynamic motions for robotic manipulators with geometric path constraints

This paper presents a new method to plan minimum cost movements for non-redundant robotic manipulators along prescribed geometric paths while tacking into account various kinodynamic constraints. The problem consists of defining the best way to follow a prescribed geometric path under several constraints, such as limitations on joint torque, jerk, acceleration or velocity, while minimizing an objective function (time transfer, mean average of joint torques, etc.). It is formulated as a non-linear optimization problem and can be then treated by any adequate mathematical optimization method. Numerical examples using genetic algorithms are presented to illustrate the effectiveness of the proposed approach.

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

[2]  Taha Chettibi,et al.  A Stochastic Off Line Planner of Optimal Dynamic Motions for Robotic Manipulators , 2004, ICINCO.

[3]  Oussama Khatib,et al.  The explicit dynamic model and inertial parameters of the PUMA 560 arm , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

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

[5]  Zvi Shiller,et al.  Time-Energy Optimal Control of Articulated Systems With Geometric Path Constraints , 1996 .

[6]  Edgard Jamhour,et al.  Planning smooth trajectories along parametric paths , 1996 .

[7]  Lakmal D. Seneviratne,et al.  Time-optimal smooth-path motion planning for a mobile robot with kinematic constraints , 1997, Robotica.

[8]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[9]  Christopher R. Houck,et al.  A Genetic Algorithm for Function Optimization: A Matlab Implementation , 2001 .

[10]  E. Croft,et al.  Smooth and time-optimal trajectory planning for industrial manipulators along specified paths , 2000 .

[11]  Peter I. Corke,et al.  A robotics toolbox for MATLAB , 1996, IEEE Robotics Autom. Mag..

[12]  Eiji Shintaku.  Minimum energy trajectory for an underwater manipulator and its simple planning method by using a Genetic Algorithm , 1998, Adv. Robotics.

[13]  Renfrey B. Potts,et al.  A discrete trajectory planner for robotic arms with six degrees of freedom , 1989, IEEE Trans. Robotics Autom..

[14]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[15]  H. Lehtihet,et al.  Minimum cost trajectory planning for industrial robots , 2004 .

[16]  Taha Chettibi,et al.  Parametric optimization for optimal synthesis of robotic systems motions , 2005, ICINCO.

[17]  Kang G. Shin,et al.  Minimum Cost Trajectory Planning for Industrial Robots , 1991 .

[18]  Nancy M. Amato,et al.  Extracting optimal paths from roadmaps for motion planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[19]  F. Yano,et al.  Preferable movement of a multi-joint robot arm using genetic algorithm , 1999 .

[20]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms , 1995 .

[21]  Friedrich Pfeiffer,et al.  A concept for manipulator trajectory planning , 1987, IEEE J. Robotics Autom..

[22]  Steven Dubowsky,et al.  Robot Path Planning with Obstacles, Actuator, Gripper, and Payload Constraints , 1989, Int. J. Robotics Res..

[23]  Z. Shiller,et al.  Computation of Path Constrained Time Optimal Motions With Dynamic Singularities , 1992 .

[24]  Aurelio Piazzi,et al.  Global minimum-jerk trajectory planning of robot manipulators , 2000, IEEE Trans. Ind. Electron..

[25]  Motoji Yamamoto,et al.  Collision free minimum time trajectory planning for manipulators using global search and gradient method , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

[26]  Lianfang Tian,et al.  An effective robot trajectory planning method using a genetic algorithm , 2004 .

[27]  Kang G. Shin,et al.  Minimum-time control of robotic manipulators with geometric path constraints , 1985 .

[28]  Jean-Jacques E. Slotine,et al.  Improving the Efficiency of Time-Optimal Path-Following Algorithms , 1988, 1988 American Control Conference.

[29]  Motoji Yamamoto,et al.  Quasi-time-optimal motion planning of mobile platforms in the presence of obstacles , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[30]  N. McKay,et al.  A dynamic programming approach to trajectory planning of robotic manipulators , 1986 .

[31]  John T. Betts.  A direct approach to solving optimal control problems , 1999, Computing in Science & Engineering.

[32]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[33]  Renfrey B. Potts,et al.  Minimum time trajectory planner for the discrete dynamic robot model with dynamic constraints , 1988, IEEE J. Robotics Autom..

[34]  T. Chettibi,et al.  Generating optimal dynamic motions for closed-chain robotic systems , 2005 .

[35]  C. Lin,et al.  Formulation and optimization of cubic polynomial joint trajectories for industrial robots , 1983 .

[36]  A. Piazzi,et al.  Global minimum-time trajectory planning of mechanical manipulators using interval analysis , 1998 .