Long-Horizon Planning and Control of Dynamic Whole-Body Locomotion
Robust long-horizon loco-manipulation on legged robots demands trajectory optimizers that are simultaneously fast, physics-faithful, and able to enforce hard constraints. Classical pseudospectral collocation promises spectral (exponential) accuracy on coarse grids—essential for planning over long time horizons—but its O(N^3) stage complexity and lack of an embedded feedback policy have prevented real-time deployment. On the other hand, existing work in Differential Dynamic Programming exhibits remarkable linear time complexity, but suffers from poor conditioning over long time horizons when using forward dynamics and has great difficulty with handling arbitrary constraints. For the first time, the paper closes that gap by introducing Pseudospectral Differential Dynamic Programming—a novel dual-layer optimal control solver that (i) reduces Radau IIA collocation to a fully decoupled block diagonal system based on a lifted Newton step using an efficient lower-triangular Ls Jacobian approximation, (ii) adopts a condensed inverse-dynamics formulation that preserves coarse-grid fidelity while eliminating state variables, (iii) handles arbitrary equality and inequality constraints with high precision via an active-set null-space Riccati recursion, and (iv) yields a stabilizing whole-body feedback controller "for free" from the same Riccati factors. The resulting solver unifies spectral accuracy, linear scalability, rigorous constraint handling, and closed-loop robustness, all of which are key ingredients for real-time, long-horizon model-predictive control of agile legged platforms.
Advisor: Professor Mahdi Agheli (WPI)
Committee: Professor Guanrui Li (WPI) and Ludovic Righetti, Ph.D. (NYU)