Maximum load carrying capacity of mobile manipulators: optimal control approach

In this paper, finding the maximum load carrying capacity of mobile manipulators for a given two-end-point task is formulated as an optimal control problem. The solution methods of this problem are broadly classified as indirect and direct. This work is based on the indirect solution which solves the optimization problem explicitly. In fixed-base manipulators, the maximum allowable load is limited mainly by their joint actuator capacity constraints. But when the manipulators are mounted on the mobile bases, the redundancy resolution and nonholonomic constraints are added to the problem. The concept of holonomic and nonholonomic constraints is described, and the extended Jacobian matrix and additional kinematic constraints are used to solve the extra DOFs of the system. Using the Pontryagin's minimum principle, optimality conditions for carrying the maximum payload in point-to-point motion are obtained which leads to the bang-bang control. There are some difficulties in satisfying the obtained optimality conditions, so an approach is presented to improve the formulation which leads to the two-point boundary value problem (TPBVP) solvable with available commands in different softwares. Then, an algorithm is developed to find the maximum payload and corresponding optimal path on the basis of the solution of TPBVP. One advantage of the proposed method is obtaining the maximum payload trajectory for every considered objective function. It means that other objectives can be achieved in addition to maximize the payload. For the sake of comparison with previous results in the literature, simulation tests are performed for a two-link wheeled mobile manipulator. The reasonable agreement is observed between the results, and the superiority of the method is illustrated. Then, simulations are performed for a PUMA arm mounted on a linear tracked base and the results are discussed. Finally, the effect of final time on the maximum payload is investigated, and it is shown that the approach presented is also able to solve the time-optimal control problem successfully.

[1]  Motoji Yamamoto,et al.  Trajectory planning of mobile manipulator with end-effector's specified path , 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).

[2]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[3]  G. Bessonnet,et al.  Optimal dynamics of actuated kinematic chains. Part 2: Problem statements and computational aspects , 2005 .

[4]  Homayoun Seraji,et al.  A Unified Approach to Motion Control of Mobile Manipulators , 1998, Int. J. Robotics Res..

[5]  D. Hull.  Conversion of optimal control problems into parameter optimization problems , 1996 .

[6]  H. Ghariblu,et al.  Maximum allowable load on wheeled mobile manipulators imposing redundancy constraints , 2003, Robotics Auton. Syst..

[7]  Bahram Ravani,et al.  DYNAMIC LOAD CARRYING CAPACITY OF MECHANICAL MANIPULATORS-PART II: COMPUTATIONAL PROCEDURE AND APPLICATIONS , 1988 .

[8]  Lorenzo Casalino,et al.  Genetic Algorithm and Indirect Method Coupling for Low-Thrust Trajectory Optimization , 2006 .

[9]  E. Bertolazzi,et al.  Symbolic–Numeric Indirect Method for Solving Optimal Control Problems for Large Multibody Systems , 2005 .

[10]  Alonzo Kelly,et al.  Reactive Nonholonomic Trajectory Generation via Parametric Optimal Control , 2003, Int. J. Robotics Res..

[11]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[12]  Moharam Habibnejad Korayem,et al.  Maximum allowable load of mobile manipulators for two given end points of end effector , 2004 .

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

[14]  Terrance L. Huntsberger,et al.  Autonomous multirover system for complex planetary surface retrieval operations , 1997, Other Conferences.

[15]  Bahram Ravani,et al.  Dynamic Load Carrying Capacity of Mechanical Manipulators—Part I: Problem Formulation , 1988 .

[16]  Motoji Yamamoto,et al.  Sub-optimal trajectory planning of mobile manipulator , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[17]  Jasbir S. Arora,et al.  12 – Introduction to Optimum Design with MATLAB , 2004 .

[18]  Kai H. Luo,et al.  45th AIAA/ASME/SAE/ASEE joint propulsion conference & exhibit , 2009 .

[19]  Motoji Yamamoto,et al.  Trajectory planning of mobile manipulator with stability considerations , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[20]  Moharam Habibnejad Korayem,et al.  Trajectory optimization of flexible mobile manipulators , 2005, Robotica.

[21]  Ahmad Ghasempoor,et al.  A measure of machine stability for moving base manipulators , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[22]  W. Szyszkowski,et al.  Improving Time-Optimal Maneuvers of Two-Link Robotic Manipulators , 2000 .

[23]  James E. Bobrow,et al.  Payload maximization for open chained manipulators: finding weightlifting motions for a Puma 762 robot , 2001, IEEE Trans. Robotics Autom..

[24]  Moharam Habibnejad Korayem,et al.  Analysis of wheeled mobile flexible manipulator dynamic motions with maximum load carrying capacities , 2004, Robotics Auton. Syst..

[25]  Li-Qun Chen,et al.  Optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation , 2006, Appl. Math. Comput..

[26]  Evangelos Papadopoulos,et al.  On Path Planning and Obstacle Avoidance for Nonholonomic Platforms with Manipulators: A Polynomial Approach , 2002, Int. J. Robotics Res..

[27]  D. A. Rey,et al.  Online automatic tipover prevention for mobile manipulators , 1997, Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems. Innovative Robotics for Real-World Applications. IROS '97.

[28]  W. Szyszkowski,et al.  An Algorithm for Time-Optimal Control Problems , 1998 .

[29]  T. Chettibi,et al.  Optimal motion planner of mobile manipulators in generalized point-to-point task , 2006, 9th IEEE International Workshop on Advanced Motion Control, 2006..

[30]  Paolo Fiorini,et al.  An autonomous robot for indoor light logistics , 2004, 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566).

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

[32]  Zvi Shiller,et al.  Time-energy optimal control of articulated systems with geometric path constraints , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.