Optimal motion planning of redundant planar serial robots using a synergy-based approach of convex optimization, disjunctive programming and receding horizon

Abstract

This paper is focused on the optimal motion planning of redundant planar serial robots, by avoiding obstacles within its workspace. A synergy-based algorithm between convex optimization, disjunctive programming and receding horizon is proposed to the end of achieving advantages such as finding the global optimum solution and low computational time. For the purpose of the problem, different cost functions can be considered, including among others, transition time, energy usage or path length. In addition, kinematic and dynamic relations of the robots under study are expressed as constraints of the problem and since they are non-convex functions, they are approximated by convex constraints. The proposed algorithm is simulated for 3-DOF and 4-DOF redundant planar serial robots in the presence of static and dynamic obstacles using the CVX package in MATLAB and the Gurobi optimization package in the Qt Creator environment. Finally, the proposed approach is implemented on a real 4-DOF planar serial robot via the Gurobi optimization package using the C++ programming language. Results reveal that using a moving horizon is a proper and reliable method to be used for real-time purposes compared with other approaches suggested in the literature. The average computational time at each step is less than 0.3 seconds.