Space-time functional gradient optimization for motion planning

Functional gradient algorithms (e.g. CHOMP) have recently shown great promise for producing locally optimal motion for complex many degree-of-freedom robots. A key limitation of such algorithms is the difficulty in incorporating constraints and cost functions that explicitly depend on time. We present T-CHOMP, a functional gradient algorithm that overcomes this limitation by directly optimizing in space-time. We outline a framework for joint space-time optimization, derive an efficient trajectory-wide update for maintaining time monotonicity, and demonstrate the significance of T-CHOMP over CHOMP in several scenarios. By manipulating time, T-CHOMP produces lower-cost trajectories leading to behavior that is meaningfully different from CHOMP.