Covariant Hamiltonian Optimization for Motion Planning

A trajectory-optimization planner that uses gradient descent to push an initial trajectory away from obstacles while keeping it smooth.

CHOMP was proposed by CMU's Ratliff, Zucker, Bagnell, and Srinivasa at ICRA 2009, with an extended version in IJRR in 2013. It discretizes a trajectory into a sequence of waypoints, with cost split into two terms: a smoothness term (the sum of squared velocity and acceleration computed by finite differences), and an obstacle term (approximating the robot as a string of small spheres and querying a signed distance field of the environment — the closer to an obstacle, the higher the cost). ‘Covariant’ refers to premultiplying the gradient update by the inverse of a smoothness metric matrix, so a single change spreads smoothly across the whole trajectory rather than yanking a single waypoint; ‘Hamiltonian’ in the name refers to using Hamiltonian Monte Carlo plus random perturbation to escape local optima. It doesn't require the initial trajectory to be collision-free — it can converge starting from a straight line that passes right through an obstacle. Its drawback is getting stuck in local optima, occasionally cutting straight through a thin obstacle, so it's often given a collision-free initial guess from a sampling planner such as OMPL first. It belongs, alongside STOMP and TrajOpt, to the family of optimization-based motion planners.

ExampleThe original paper used it for manipulation planning on a Barrett WAM arm, and also to generate walking trajectories for the LittleDog quadruped robot. MoveIt integrates CHOMP, with smoothness_cost_weight and obstacle_cost_weight as tunable parameters balancing smoothness against obstacle avoidance.

Also called

CHOMP, CHOMP Planner

Related

Trajectory Optimization · STOMP · TrajOpt · Signed Distance Field / Function · MoveIt Motion Planning Framework · Path Smoothing (Shortcutting)

Sources

Ratliff, Zucker, Bagnell, Srinivasa: CHOMP: Gradient Optimization Techniques for Efficient Motion Planning (ICRA 2009)
Zucker et al., CHOMP: Covariant Hamiltonian Optimization for Motion Planning (IJRR 2013)
MoveIt: CHOMP Planner 教程 (Chinese)