Planning

caliper-planning is a pure-CPU, dependency-light motion-planning crate. It plans collision-free joint-space waypoint paths and, on request, retimes them into playable trajectories.

Sampling-based planners

• RRT-Connect — bidirectional, joint-space, with caliper_collision::CollisionModel (self + world) plus joint limits as the validity check. This is the default planner (Planner).
• RRT* — the asymptotically-optimal variant (rrtstar).
• PRM — a probabilistic roadmap (prm).

All three are deterministic: they use a seeded splitmix64 PRNG (no rand), so a given seed yields the same plan every time and the planners are fully unit-testable with no hardware.

Smoothing and retiming

A raw sampled path is jagged. Planner shortcut-smooths the result (repeatedly attempting to replace sub-paths with collision-free straight-line shortcuts). To play or record the plan, Planner::plan_trajectory (via the motion crate's retime) turns the collision-free waypoint path into a jerk-limited caliper_motion::Trajectory.

Reachability

caliper_planning::reach provides reachability analysis — a three-way classification of goals as reachable / blocked / out-of-reach that is collision-aware.

Trajectory optimization (CHOMP)

caliper-trajopt is a separate, CHOMP-style collision-aware trajectory optimizer. Given an initial waypoint path, it refines the interior waypoints (endpoints held fixed) by gradient descent on

cost(path) = w_smooth · smoothness(path) + w_obs · obstacle(path)

• smoothness is the classic CHOMP quadratic — summed squared finite-difference accelerations ‖q[i-1] − 2·q[i] + q[i+1]‖² over the interior. Its analytic gradient (the pentadiagonal AᵀA q form) is cross-validated in the tests against a finite-difference of the cost.
• obstacle is a smooth proximity penalty: each robot collider is reduced to a body sphere, placed by FK and inflated by its bounding radius, and scored against an ObstacleField signed-distance field with the standard CHOMP hinge potential.

How planning is verified

The planners and smoothing are re-derived-correct but self-consistent-only. The important honesty here is the nature of the collision guarantee: it is a sampled-at-resolution guarantee. The planner checks configurations at a discrete resolution along each edge, so a sufficiently narrow passage can be tunneled — the plan can be reported collision-free while a thin obstacle slips between samples. There are also no dedicated narrow-passage / near-π / at-limit stress fixtures yet; coverage is random sampling. These are documented limitations, not defects.