Accelerating Trajectory Optimization by Exploiting B-Spline Gradient Structure

Abstract

This work presents a discrete-time trajectory optimization framework that achieves near real-time performance for robotic manipulators. This is achieved by drastically speeding up constraint gradient computations. The approach leverages the analytical and structural properties of B-splines to introduce three key speedups: exploiting gradient sparsity from local control, using a hybrid-analytical method to replace most finite differences with closed-form derivatives, and aggregating constraints per knot-span to reduce the problem size. Validated on a simulated UR5e across 64 tasks in a cluttered workspace, these cumulative speedups reduce computation time by up to 96.3% (a 26.9x speedup) relative to a finite-difference baseline, without compromising trajectory quality, success rate, or fidelity to kinematic, dynamic, and collision constraints.