Accelerating Trajectory Optimization by Exploiting B-Spline Gradient Structure
Nikos Doiron, Thomas Duquette, Gilde Vanel Tchane Djogdom, Andre Gallant
AI summary
Problem
Discrete-time trajectory optimization for robotic manipulators is computationally demanding due to expensive gradient evaluations, limiting real-time re-planning and adaptation in dynamic environments.
Approach
The framework accelerates Sequential Quadratic Programming (SQP) solvers by exploiting B-spline local control for gradient sparsity, using hybrid analytical derivatives, and aggregating constraints per knot-span to reduce problem size.
Key results
- Up to 96.3% reduction in computation time (26.9x speedup) over finite-difference baseline
- Maintains trajectory quality, success rate, and constraint fidelity across 64 simulated UR5e tasks
- Enables near real-time trajectory optimization for serial manipulators in cluttered workspaces
- Reduces optimization problem size by aggregating constraints per knot-span without sacrificing accuracy
Why it matters
Enables fast, constraint-compliant motion planning for industrial robots, making real-time adaptation to dynamic environments practically feasible.
Abstract
This work presents a discrete-time trajectory opti- mization 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.