Time Parameterization

Attaching a timing schedule to a purely geometric path, deciding when each point is reached and how fast.

Many motion planners — including the OMPL sampling-based planners that MoveIt calls — output only a sequence of joint waypoints with no timing information: a purely geometric path q(s), where s runs from 0 to 1 as progress along the path. Time parameterization finds a function s(t) that assigns a timestamp, velocity, and acceleration to each waypoint so the robot can actually execute it. By the chain rule, q̇ = q′(s)·ṡ and q̈ = q′(s)·s̈ + q″(s)·ṡ², so joint velocity and acceleration limits translate directly into constraints on ṡ and s̈. It only decides how fast to move, not which path to take — that is what distinguishes it from trajectory optimization. Common algorithms include the iterative parabolic method, time-optimal trajectory generation (TOTG, by Tobias Kunz and Mike Stilman, RSS 2012), TOPP-RA, and the jerk-limited Ruckig. MoveIt currently defaults to TOTG and provides velocity- and acceleration-scaling factors from 0 to 1 to slow the whole motion down.

ExamplePlanning an arm's motion from A to B in MoveIt, OMPL returns a sequence of joint waypoints with no timing; TOTG then assigns timestamps to them based on the velocity and acceleration limits in joint_limits.yaml. Setting the velocity scaling factor to 0.1 computes the joint speed limits at 10% of their original values.

Also called

Trajectory Time Parameterization, Retiming

Related

Time-Optimal Path Parameterization · TOPP-RA · Ruckig · Trajectory Planning · Trapezoidal Velocity Profile · MoveIt Motion Planning Framework

Sources

MoveIt Documentation: Time Parameterization
Kunz, Stilman: Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity (RSS 2012)