Interaction-Stiffness-Guided Basis Allocation in Dynamic Movement Primitives for Efficient Skill Transfer
Authors: Chan Xu, Silu Chen, Dehao Wang, Xiyu Chen, Dexin Jiang, Chi Zhang, Guilin Yang, Chenguang Yang, +1 more
Organizations: Zhejiang Key Laboratory of Precision Actuation and Intelligent Robotics, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China · University of Chinese Academy of Sciences, Beijing 100049, China · Department of Computing, The Hong Kong Polytechnic University, HKSAR, China
Dynamic Movement Primitives (DMPs) provide a compact and stable formulation for trajectory representation and generalization in robot skill learning. However, their predefined basis layout limits the allocation of approximation capacity according to stage-dependent precision requirements. To address this issue, this article proposes Stage-Criticality-Guided Dynamic Movement Primitives (SC-DMPs) with adaptive basis allocation for precision-critical skill learning. Operator-robot interaction stiffness and a trajectory-consistency cue derived from cross-demonstration task-space variability are integrated to construct a stage-criticality index. Guided by this index, basis centers are redistributed in normalized time through inverse cumulative criticality and mapped to the canonical phase domain, while their bandwidths are refined to adjust local approximation support. This enables denser and more flexible representation at high-criticality stages while retaining sparser allocation elsewhere. Experiments on handwriting trajectories and three real-robot tasks show that the inferred criticality is concentrated in geometrically demanding and task-constrained regions. Comparisons with DMPs, ProMPs, ProDMP, GP-MP, and KMP demonstrate improved trajectory reproduction, endpoint generalization, and task-critical accuracy while retaining a compact model and the stable structure of classical DMPs.
Figures & tables
Symbol
Description
M , T , D
Number of demonstrations, number of aligned time steps, and task-space dimension, respectively.
ti
Normalized time at the i -th aligned time step.
Pi,m , Ki,m , Qi,m
Task-space position, axis-wise interaction stiffness, and their concatenated motion-state vector.
NG , πj , μj , Λj
Number of Gaussian components and the weight, mean, and covariance of the j -th component.
γj(t) , ΛQt,j , ΛQQ,j
Posterior responsibility and covariance blocks used in GMR conditioning.
Pˉ(t) , Kˉ(t) , σP2(t)
GMR reference trajectory, stiffness profile, and task-space variability.
TABLE I: Summary of main symbols.
Fig. 1: Overall framework of the proposed SC-DMPs. Operator-robot interaction stiffness and cross-demonstration task-space variability are used to estimate a stage-criticality index, which guides basis-center redistribution and adaptive bandwidth design for precision-critical skill reproduction.
Fig. 2: Experimental platform for interaction stiffness identification.
Fig. 3: Handwriting letter data acquisition. (a)-(c) present the template, the trajectory with stiffness ellipsoids, and the visualized stage-criticality index for letter “Z”. (d)-(f) show the corresponding results for letter “M”.
Fig. 4: Learning errors of SC-DMPs and DMPs for “Z” under 5, 10, 15, 20, 25, and 30 basis functions on a logarithmic scale. (a) RMSE (mm). (b) W-RMSE (mm). (c) RMSE-Geo (mm). (d) MaxE (mm).
Fig. 5: Learning errors of SC-DMPs and DMPs for “M” under 5, 10, 15, 20, 25, and 30 basis functions on a logarithmic scale. (a) RMSE (mm). (b) W-RMSE (mm). (c) RMSE-Geo (mm). (d) MaxE (mm).
Errors
Mean reduction
95% confidence interval
Adjusted p
RMSE
21.42% ± 10.11%
[13.99%, 25.65%]
0.0103
W-RMSE
21.92% ± 10.27%
[13.99%, 26.08%]
0.0103
RMSE-Geo
32.50% ± 13.89%
[23.55%, 38.91%]
0.0020
MaxE
24.67% ± 20.16%
[8.57%, 32.56%]
0.0122
TABLE II: Statistical analysis of SC-DMPs versus DMPs across different basis-function settings.
Fig. 6: Center distributions under 15 and 30 basis functions, where color intensity increases with density. (a) and (c) correspond to “Z”. (b) and (d) correspond to “M”.
Fig. 7: Comparison of learning performance between SC-DMPs and DMPs. (a) and (b) correspond to “Z” with 15 and 30 basis functions. (c) and (d) correspond to “M” with 15 and 30 basis functions.
Fig. 8: Ablation results of basis representation with 20 basis functions. (a) RMSE (mm). (b) RMSE-Geo (mm). (c) MaxE (mm).
Fig. 9: Ablation results of stage-criticality construction with 20 basis functions. (a) RMSE (mm). (b) RMSE-Geo (mm). (c) MaxE (mm).
Letter
Refinement method
Temporal-variation reduction (%)
Critical-stage retention (%)
Construction time (s)
“Z”
Prior-only
0.00
100.00
<0.001
Prior-smoothed
3.24
99.00
0.008
STR-Net-refined
20.91
91.50
1.258
“M”
Prior-only
0.00
100.00
<0.001
Prior-smoothed
3.21
100.00
<0.001
STR-Net-refined
34.92
85.00
1.147
TABLE III: Stage-criticality refinement characteristics and construction time.
Fig. 10: Endpoint-generalization errors for “Z” under varying numbers of basis functions. (a) NSE. (b) W-RMSE (mm). (c) RMSE-Geo (mm).
Fig. 11: Endpoint-generalization errors for “M” under varying numbers of basis functions. (a) NSE. (b) W-RMSE (mm). (c) RMSE-Geo (mm).
Fig. 12: Endpoint-generalization of DMPs and SC-DMPs on “Z” with 20 basis functions. (a) Translation. (b) Start-point change. (c) Goal-point change. (d) Start-point and goal-point changes.
Fig. 13: Spatial-scaling generalization of DMPs and SC-DMPs on “Z” with 20 basis functions. (a) 0.5 × . (b) 2 × . (c) 3 × . (d) 5 × .
Letter
Scale
NSE
W-RMSE (mm)
RMSE-Geo (mm)
DMPs
SC-DMPs
DMPs
SC-DMPs
DMPs
SC-DMPs
“Z”
0.5×
0.0055
0.0048
0.9063
0.7465
1.3508
1.0256
2×
0.0055
0.0048
3.6251
2.9858
5.4032
4.1025
3×
0.0055
0.0048
5.4377
4.4787
8.1048
6.1537
5×
0.0055
0.0048
9.0628
7.4645
13.5080
10.2562
Reduction
12.99%
17.64%
24.07%
TABLE IV: Errors under spatial-scaling generalization.
Letter
Method
Learning performance
Endpoint generalization
Computational efficiency
RMSE (mm)
RMSE-Geo (mm)
NSE
RMSE-Geo (mm)
Model size (kB)
Adaptation time (ms)
“Z”
DMPs
0.7936
1.2318
0.0027
1.3303
1.00
4.77
ProMPs
0.6136
0.8083
0.8927
68.3981
29.08
0.75
ProDMP
0.6396
0.9263
0.1004
32.1902
0.99
1.66
GP-MP
1.1117
1.3649
0.2599
68.2537
9.65
89.86
KMP
20.6595
16.8022
0.1696
63.0821
65.64
938.29
TABLE V: Comparison of learning performance, endpoint generalization, and computational efficiency on letter trajectories.
Expert demonstrations are widely assumed to be the gold standard for robot imitation learning. Yet for fine-grained manipulation such as insertion, stacking, and alignment, we uncover a counterintuitive failure mode: fluent demonstrations can be poor teachers. A skilled teleoperator compresses the decisive moments of alignment and recovery into a brief temporal window, leaving the policy flooded with redundant free-space motion and starved of supervision exactly where precision determines success. We address this bottleneck at two levels. At the data level, slowing down near alignment and resampling critical segments both help, yet the gain comes mainly from broadening the coverage of recovery states the policy must learn, not from reweighting frames it already has. Such data-side fixes, however, leave the policy's per-frame view untouched: a single image still maps directly to an action, and the local motion that governs correction stays implicit. We therefore turn to the representation level and introduce STAIR (\textbf{S}patio-\textbf{T}emporal feature \textbf{A}s an \textbf{I}nterface for \textbf{R}obot learning), a compact dynamic feature that bridges the vision-language model and the action expert, distilling the short-horizon motion already recorded in each trajectory into dense, motion-aware supervision. Trained on fluent data alone, STAIR recovers most of the deliberate-demonstration gain (50.0 to 62.2% overall, approaching the 64.4% of deliberate demonstrations). These results call for a more pedagogical view of robot data, optimized for machine learnability rather than human efficiency alone.
Mingyu Liu, Zeju Li, Jiuhe Shu +4
Zhejiang University · Hong Kong University of Science and Technology (GZ) · Shanghai Innovation Institute
Recent advances in 3D Gaussian Splatting (3DGS) have enabled visually realistic demonstration generation from a single expert trajectory and a short multi-view scan. However, existing 3DGS-based synthesis pipelines typically generate new motions using sampling-based planners or trajectory optimization, which often deviate substantially from the expert's demonstrated path. While such deviations may be acceptable for tasks insensitive to motion shape, they discard subtle spatial and temporal structure that is critical for contact-rich and shape-sensitive manipulation, causing increased demonstration diversity to harm downstream policy learning. We argue that demonstration synthesis should treat the expert trajectory as a strong prior. Building on this principle, we propose a framework that synthesizes diverse task demonstrations while explicitly preserving expert motion structure. We model the expert trajectory using Dynamic Movement Primitives (DMPs) and retarget it to new goals, object configurations, and viewpoints within a reconstructed 3DGS scene, yielding phase-consistent, shape-preserving motion by construction. To safely realize this expert-preserving diversity in cluttered scenes, we introduce an analytic obstacle-aware DMP formulation that operates directly on the continuous density field induced by the 3DGS representation. This enables collision avoidance while minimally perturbing the nominal expert motion, unifying photorealistic rendering and geometric reasoning without additional scene representations. We evaluate our approach on a Spot mobile manipulator across three manipulation tasks with increasing sensitivity to trajectory fidelity. Compared to planner- and optimization-based synthesis, our method produces trajectories with lower deviation and collision rates and yields higher task success when training diffusion-based visuomotor policies.
Moniruzzaman Akash, Momotaz Begum
Department of Computer Science · University of New Hampshire
We present a primitive-informed sampling-based model predictive control (MPC) framework for multi-fingered dexterous manipulation. Sampling-based MPC evaluates candidate control trajectories through forward simulation without requiring gradients through complex contact dynamics. However, directly sampling these trajectories in the high-dimensional joint space of a dexterous hand is inefficient and makes performance strongly dependent on the sampling distribution. Our framework biases sampling using low-dimensional manipulation primitives that encode coordinated finger motions, while simultaneously optimizing joint-level residuals to adapt these motions to the current hand-object configuration. Task-related rollout constraints reject infeasible trajectories during forward simulation, improving the effective use of the sampling budget. We evaluate the approach on a 16 DoF Allegro hand using a synchronized MuJoCo digital twin. Ablations show that both the primitive and residual are necessary for reliable continuous in-hand rotation, that increasing the sampling budget alone does not recover this coordination, and that rollout constraints substantially improve success rate. A primitive extracted for one object size transfers to other sizes and remains effective under model mismatch. The framework further supports grasping, object reorientation, and coordinated arm-hand manipulation, using primitives extracted from both a simulation-trained policy and human hand-motion data.
Emek Barış Küçüktabak, Karankumar Patel, Jinda Cui +3
Honda Research Institute USA, San Jose, CA, USA · Georgia Institute of Technology, Atlanta, GA, USA (Work done during an internship at HRI)