State Parameterization Basic Spline Functions for Trajectory Optimization

Abstract

An important type of basic functions named basis spline (B-spline) is provided a simpler approximate and more stable approach to solve problems in optimal control. Furthermore, it can be proved that with special knot sequence, the B-spline basis are exactly Bernstein polynomials. The approximate technique is based on state variable is approximate as a linear combination of B-spline then anon linear optimization problem is obtained and the optimal coefficients are calculated using an iterative algorithm. Two different examples are tested using the proposed algorithm.