Optimal path planning of manipulators with singular configurations, workspace and collision-free constraints

Abstract

This paper presents an optimal control approach for the off-line path planning of manipulators with a large number of non-convex constraints relating the kinematic performances and the environmental limits. The main contribution is in the analysis of the singular configurations and workspace of manipulators in dynamical path planning problem, the development of a new method for three-dimensional collision avoidance of revolute manipulators in an environment clustered with obstacles defined by convex surfaces, and the use of the augmented Lagrangian for the numerical solution of this highly nonlinear and nonconvex path planning problem. This approach is based on the formulation of all these constraints as special state space constraints, in the form of inequalities, and the path planning problem as an optimal control problem. The solution is then obtained by UZAWA’s algorithm. Some simulation results are presented for the 3-dof robot PAMIR built at ESIEE by P. Durand and F. Viette for the purpose of research and education [1].