Efficient Bezier Velocity Optimization for Free-Floating Space Manipulators

Summary

Abstract Summary

We present FAVOR (Free-floating Arm Velocity Optimization with Recursive Sensitivities), a planner for collision-free reaching, tracking, and prescribed-time pre-grasp interception on an unactuated spacecraft. It optimizes Bezier joint-velocity curves with linear velocity, acceleration, and continuity constraints. Decision dimension is independent of rollout resolution. Analytical recursive sensitivities provide task and clearance gradients through the coupled base-arm motion. Parallel evaluation, caching, and incremental collision discovery reduce computation. With a seven-DoF arm and five simulated spacecraft models, FAVOR achieves 99.8% point-to-point success with 1.779 s mean computation, versus 62.9% and 50.270 s for an IK-initialized position-spline baseline. Means include failures and timeouts. FAVOR completes 30 of 36 tracking cases, versus 15 for single-step QP, and all 36 interception instances, versus 22 for the spline baseline. A controlled ablation shows that finite differences increase mean planning time 4.7-fold.

Key Points

We present FAVOR (Free-floating Arm Velocity Optimization with Recursive Sensitivities), a planner for collision-free reaching, tracking, and prescribed-time pre-grasp interception on an unactuated spacecraft.
It optimizes Bezier joint-velocity curves with linear velocity, acceleration, and continuity constraints.
Decision dimension is independent of rollout resolution
Analytical recursive sensitivities provide task and clearance gradients through the coupled base-arm motion.
Parallel evaluation, caching, and incremental collision discovery reduce computation

Model and Planning Formulation

Consider an $n$-DoF arm mounted on an unactuated spacecraft. No external wrench acts during the planned maneuver, so the total linear and angular momenta, $P_{0},H_{0}\in\mathbb{R}^{3}$, are conserved. Angular momentum $H_{0}$ is measured about the fixed inertial origin. Let $r_{b}$ and $R_{b}\in SO(3)$ be the base position and attitude, and let $\theta\in\mathbb{R}^{n}$ denote the joints.

Base linear and angular velocities are expressed in the inertial frame.

Model and Planning Formulation — Efficient Bezier Velocity Optimization for Free-Floating Space Manipulators — (a) CALIPSO

Trajectory Optimization

The robot model and conserved momenta $(P_{0},H_{0})$ are fixed. The changing momentum map couples each state to preceding joint commands.

Writing the components of ( 2 ) as $(v_{b,k},\omega_{b,k})$, the simulator propagates the configuration by Together, these updates define the discrete state-transition map $q_{k+1}=F(q_{k},u_{k},\Delta t)$, with the updated rotation expressed in the attitude coordinates $\eta_{b,k+1}$.

Trajectory Optimization — Efficient Bezier Velocity Optimization for Free-Floating Space Manipulators — (b) Landsat 7

Evaluation

The simulator couples a seven-DoF Kinova Gen3-derived arm and Robotiq 2F-85 gripper to a freely translating and rotating base with CloudSat geometry. It includes link kinematics, masses, inertias, and self- and environment-collision models. We evaluate endpoint planning, inspection tracking, and prescribed-time pre-grasp interception.

For endpoint planning and interception, FAVOR enforces the prescribed initial joint velocity and arm-position limits of $[-2\pi,2\pi]$ rad. Base coordinates are unbounded.

Evaluation — Efficient Bezier Velocity Optimization for Free-Floating Space Manipulators — (c) Hubble

Sources and Demonstrations

Figures are reproduced from Zhang et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.