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.

Authors

• Arunkumar Byravan
• Byron Boots
• Siddhartha S. Srinivasa
• Dieter Fox

Keywords

• Trajectory
• Robots
• Timing
• Optimization
• Planning
• Collision avoidance
• Vectors
• Path Planning
• Cost Function
• Local Optimum
• Smoothing
• Objective Function
• Optimal Control
• Local Minima
• Smooth Function
• Parametrized
• Taylor Series
• Velocity Profile
• Numerical Instability
• First-order Conditions
• Time Trajectories
• Trajectories In Space
• Basin Of Attraction
• Path In Space
• Active Constraints
• Equal Spacing
• Velocity Limits
• Straight-line Path
• Linear Inequality Constraints
• Motion Duration
• Optimization Problem
• Obstacle Avoidance
• General Function
• Line Integral
• Trajectory Optimization
• Maximum Velocity
• Joint Optimization