Part 6. Intelligent control, robots and biomechatronics systems

Exploiting Jacobian and Hessian of the Lagrangian sparse structure for optimal trajectory planning speed up

D. V. Zlobin

Lomonosov Moscow State University

Abstract: This paper deals with nonlinear programming problems, in which the cost function and constraints are relatively small expressions containing variables with indices.
Analysis of problem expressions dependence on indices gives sparsity structure of Jacobian and Hessian of the Lagrangian. This allows to get general formulas for calculating their non-zero elements and leads to effective numerical solving the nonlinear programming problem.

Keywords: trajectory planning, nonlinear programming, sparse Jacobian and Hessian of the Lagrangian, IpOpt, SymPy.