A global optimization approach to trajectory planning for industrial robots

A deterministic global optimization approach is proposed for the optimal trajectory planning of D-joint industrial robots. After mapping Cartesian knots into joint knots, by inverse kinematics, they are interpolated with spline functions under constraints on joint accelerations and jerks. An interval algorithm, a procedure based on interval analysis techniques, is presented to determine an optimal piecewise trajectory which globally minimizes the total travelling time. With arbitrarily sharp precision, this procedure solves the nonlinearly constrained optimization problem which is obtained using the branch-and-bound principle where the branching is performed by uniform subdivision and the bounding via interval inclusion functions. The interval algorithm, implemented in C++ with the PROFIL/BIAS libraries, has been applied to the optimal four-spline planning of a 6-joint arm, and computational results are included.