NURBS-Based Sequential Convex Programming for Onboard Trajectory Optimization

This article proposes an enhanced approach to sequential convex programming for optimizing onboard trajectories by incorporating nonuniform rational basis splines (NURBS) curves. The contributions of the proposed method are threefold. First, it effectively reduces the number of optimization variables by utilizing NURBS curves as representations for control variables. Second, the convex-hull property of NURBS curves enables the replacement of the control inequality constraints with those defined by NURBS control points, leading to a significant reduction in the overall number of constraints. Finally, the integration of the homotopy approach with NURBS curves offers increased flexibility in shaping the curves and facilitates the solution of optimization problems involving bang-bang optimal control. Numerical demonstrations are provided to illustrate the effectiveness and efficiency of the proposed approach for onboard applications.