A novel coordinate transformation for obstacle avoidance and optimal trajectory planning

This paper presents a sequential optimization technique for the design of optimal trajectories while minimizing a cost index subject to system dynamics, path and actuation constraints. A novel coordinate transformation is introduced to cast the non-convex trajectory generation problem as a convex optimization problem. A sequential linear programming approach is discussed to solve the resulting nonlinear optimal control problem. Linearizing the system model about nominal trajectories results in a linear programming problem which is used to select a perturbation to the nominal control to satisfy the boundary conditions and the state and control constraints. Sequential solution of linear programming problem where the linearized system and control influence matrices are time varying results in the optimal control.