A sensitivity approach to optimal spline robot trajectories

Abstrnct-A robot trajectory planning problem is considered. Using smooth interpolating cubic splines as joint space trajectories, the path is parameterized in terms of time intervals between knots. A minimum time optimization problem is formulated under maximum torque and velocity constraints, and is solved by means of a first order derivative-type algorithm for semi-infinite nonlinear programming. Feasible directions in the parameter space are generated using sensitivity coefficients of the active constraints. Numerical simulations are reported for a two-link Scara robot. The proposed approach can be used for optimizing more general objective functions under different types of constraints.