State parameterization basic spline functions for trajectory optimization

Abstract EN

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 Bspline 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.