GRASP: Gradient-Guided Sampling for Contact-Rich Physics-Based Motion Retargeting
Organizations: School of Engineering and Applied Sciences, Harvard University
Abstract
We study physics-based retargeting of human demonstrations for robot learning: finding robot controls that reproduce reference motions under contact dynamics. We propose GRASP (Gradient Recovery from Archived Samples for Proposals), which combines sampling-based exploration with gradient-guided refinement without requiring a differentiable simulator. GRASP-TO extends tempered sequential Monte Carlo by fitting local quadratic cost models to archived rollouts and using their gradients to guide Markov chain Monte Carlo rejuvenation. Metropolis-Hastings correction preserves the target distribution for each fixed proposal kernel, and a population analysis connects the recovered gradients to Gaussian smoothing. GRASP-MPC scales this optimizer to long demonstrations through warm-started receding-horizon planning. Experiments on dexterous hands and humanoids show accurate retargeting with a shared tracking objective and no task-specific contact rewards, including 92.8% success on 1352 bimanual OakInk2 demonstrations. The refined references improve PPO tracking in pen spinning and humanoid-object interaction. We also demonstrate dexterous manipulation and whole-body humanoid motion on real hardware.
Figures & tables
| Method | Succ. (%) | (m) | (rad) |
|---|---|---|---|
| Dex-retargeting [ 40 ] | 28.6 | 0.08 | 0.62 |
| SPIDER [ 35 ] mjwp | 71.4 | 0.04 | 0.57 |
| SPIDER [ 35 ] mjwp_act | 77.1 | 0.04 | 0.42 |
| Do-as-I-Do [ 34 ] (Sharpa) | 81.0 | 0.03 | 0.15 |
| w/o transition reward | 79.0 | 0.03 | 0.14 |
| annealed sampling only | 72.0 | 0.08 | 0.32 |
| Hand | Finger DoF | Tasks | Succ. (%) | (cm) | (rad) |
|---|---|---|---|---|---|
| Sharpa | 22 | 1352 | 94.2 | 2.87 / 2.17 | 0.117 / 0.090 |
| Wuji | 20 | 1352 | 92.4 | 2.87 / 2.02 | 0.117 / 0.086 |
| XHand | 12 | 1352 | 95.0 | 2.87 / 2.08 | 0.112 / 0.088 |
| ADD-AUC (%) | ||||
| Method | Split | # Demos | # Objects | Sharpa |
| SPIDER [ 35 ] | Right hand | 2,718 | 33 | 40.74 |
| GRASP | All | 5,400 | 33 | 81.54 |
| Right hand | 2,117 | 33 | 84.87 | |
| Left hand | 1,213 | 33 | 85.44 | |
| Bimanual | 2,070 | 33 | 75.83 |
| Robot | Object | ||||||
|---|---|---|---|---|---|---|---|
| Robot | Data | Method | |||||
| G1 | LAFAN1 | GMR [ 1 ] | 1.08 | 2.01 | 2.40 | – | – |
| SPIDER [ 35 ] | 0.58 | 0.11 | 0.07 | – | – | ||
| GRASP | 0.30 | 0.02 | 0.06 | – | – | ||
| G1 | AMASS | GMR [ 1 ] | 6.2 | 4.1 | 18.7 | – | – |
| SPIDER [ 35 ] | 0.75 | 0.23 | 0.08 | – | – | ||
| Setting | Value |
|---|---|
| Timing | 0.005 s simulation step; 0.2 s knot spacing |
| MPC window | Up to 15 knots; commit count |
| Particles | in Table 1 ; for all hands in Table 2 ; ESS target |
| SMC moves | 5 Markov moves per stage; at most 64 tempering stages |
| Temperature | ; s |
| Prior | Appendix 9 |
| Setting | Value |
|---|---|
| Simulator | MJWarp; direct PD control; no domain randomization |
| Timing | s simulation step; 0.1 s knot spacing |
| MPC window | 8 knots; commit count ; first knot pinned |
| Particles | ; ESS target |
| SMC moves | Surrogate MALA; full-prior preconditioner; 5 Markov moves per stage; no fixed stage cap |
| Surrogate | Rank 2; ridge ; window parameter 3 |
| Setting | Value |
|---|---|
| Problem sizes | Both tasks: , ; control dimension 1 (acrobot) or 4 (pusher-slider), giving 200 or 800 variables |
| Gradient TSMC | 3 NUTS transitions per stage; at most 8 tree doublings and 200 adaptive tempering stages |
| GRASP-TO | 99 proposals per particle and stage; at most 200 adaptive tempering stages |
| RWM-TSMC | 99 proposals per particle and stage; at most 200 adaptive tempering stages |
| Parallel-MPPI | 100 independent particles; 64 rollouts per update; 15 pusher-slider updates; acrobot updates matched to the per-particle rollout budget of rollout-based TSMC |
| Hardware | NVIDIA A100 80 GB GPU |
| Acrobot | Pusher-slider | ||||
|---|---|---|---|---|---|
| Method | Cost | Time (s) | Cost | Success | Time (s) |
| Gradient-based TSMC | 2069 | 11/11 | 3075 | ||
| GRASP-TO | 46 | 11/11 | 354 | ||
| RWM-TSMC | 39 | 1/11 | 71 | ||
| Parallel-MPPI | 2 | 0/11 | 2 | ||
| (cm) | (rad) | Wall time (min) | Success (%) | |||
|---|---|---|---|---|---|---|
| Mean | Median | Mean | Median | Median | ||
| 512 | 3.274 | 2.504 | 0.1346 | 0.1068 | 30.98 | 93.12 |
| 1024 | 3.164 | 2.301 | 0.1263 | 0.0982 | 39.43 | 92.75 |
| 2000 | 2.848 | 2.162 | 0.1165 | 0.0905 | 57.49 | 94.16 |
Motion Retargeting
Motion retargeting transfers movement across different bodies, skeletons, or robots while preserving its intent and physical feasibility.
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