Energy-Optimal Multi-Goal Motion Planning for Planar Robot Manipulators

Pierre Bonami (), Alberto Olivares () and Ernesto Staffetti ()
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Pierre Bonami: Centre National de la Recherche Scientifique
Alberto Olivares: Universidad Rey Juan Carlos
Ernesto Staffetti: Universidad Rey Juan Carlos

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 1, No 4, 80-104

Abstract: Abstract In this work, the energy-optimal motion planning problem for planar robot manipulators with two revolute joints is studied, in which the end-effector of the robot manipulator is constrained to pass through a set of waypoints, whose sequence is not predefined. This multi-goal motion planning problem has been solved as a mixed-integer optimal control problem in which, given the dynamic model of the robot manipulator, the initial and final configurations of the robot, and a set of waypoints inside the workspace of the manipulator, one has to find the control inputs, the sequence of waypoints with the corresponding passage times, and the resulting trajectory of the robot that minimizes the energy consumption during the motion. The presence of the waypoint constraints makes this optimal control problem particularly difficult to solve. The mixed-integer optimal control problem has been converted into a mixed-integer nonlinear programming problem first making the unknown passage times through the waypoints part of the state, then introducing binary variables to enforce the constraint of passing once through each waypoint, and finally applying a fifth-degree Gauss–Lobatto direct collocation method to tackle the dynamic constraints. High-degree interpolation polynomials allow the number of variables of the problem to be reduced for a given numerical precision. The resulting mixed-integer nonlinear programming problem has been solved using a nonlinear programming-based branch-and-bound algorithm specifically tailored to the problem. The results of the numerical experiments have shown the effectiveness of the approach.

Keywords: Multi-goal motion planning; Robot manipulators; Mixed-integer optimal control problem; Mixed-integer nonlinear programming; 49M37; 90C11; 68T40 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0516-0

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