Interaction-Stiffness-Guided Basis Allocation in Dynamic Movement Primitives for Efficient Skill Transfer

Can stage-wise task-criticality inferred from operator-robot interaction stiffness and cross-demonstration trajectory variability guide adaptive basis allocation in dynamic movement primitives to improve precision-critical trajectory reproduction and generalization?

Dynamic movement primitives and many movement primitives use fixed or data-independent basis/covariance layouts, so they spend approximation capacity on easy segments and under-resolve tight-tolerance stages. Existing cues such as curvature, variance, or temporal structure do not directly capture task-imposed motion tolerances, such as peg-in-hole insertion requiring high local accuracy on geometrically simple paths.

Classical DMPs place Gaussian basis centers uniformly in time. Probabilistic methods like ProMPs, ProDMP, GP-MP, and KMP adjust uncertainty or kernel hyperparameters but do not explicitly allocate local support according to precision requirements. Prior basis-refinement methods use curvature, variance, recovered temporal structure, or mutual-information timestep weights, which reflect trajectory shape or informativeness rather than task tolerance.

SC-DMPs records sEMG and robot motion during kinesthetic teaching to estimate endpoint interaction stiffness; GMM/GMR produces a reference trajectory, stiffness profile, and cross-demonstration task-space variance. A stage-criticality index fuses normalized stiffness and inverse variability and is temporally refined by a lightweight STR-Net with convolution and attention. Basis centers are placed so adjacent intervals carry equal accumulated criticality via inverse cumulative criticality, mapped to the canonical phase domain, and bandwidths are optimized by cyclic coordinate descent over discrete scaling candidates to minimize forcing-term reconstruction error.

On handwriting letters 'Z' and 'M' across 5–30 basis functions, SC-DMPs beat classical DMPs in 45 of 48 metric comparisons; mean error reductions versus DMPs were RMSE 21.42%, W-RMSE 21.92%, RMSE-Geo 32.50%, and MaxE 24.67%. Endpoint generalization was better in 34/36 comparisons; with 5 basis functions, error reductions were 21.86–35.22%. Under spatial scaling from 0.5x to 5x, reductions were NSE 12.99–18.74%, W-RMSE 17.64–25.01%, and RMSE-Geo 24.07–26.80%. Against ProMPs, ProDMP, GP-MP, and KMP, SC-DMPs achieved the lowest learning and endpoint-generalization errors for both letters, reducing learning RMSE by 3.4% and 1.6% over the best competitor for 'Z' and 'M', and endpoint-generalization RMSE-Geo by 46.1% and 23.9%. On three real-robot tasks (plug insertion/removal, sequential dipping, curved-surface wiping) with 50 basis functions, SC-DMPs reduced RMSE versus DMPs by 5.83–17.51%, RMSE-TCR by 19.93–23.86%, and MaxE-TCR by 6.56–42.01%; it achieved the lowest MaxE-TCR among all six methods. Model size was about 1 kB and adaptation time about 4.7–4.9 ms.

Authors state the method targets precision-oriented skills whose critical stages are reflected in interaction stiffness and trajectory consistency; low-stiffness compliant-critical stages, task dynamics, or environmental context would require complementary force, vision, object-dynamics, or contextual cues. Evaluation uses handwriting data with 12 demos per letter and real-robot data with only 4 demos per task on one KUKA iiwa; no physical insertion or wiping success rates are reported. Bandwidth optimization is coordinate-wise rather than globally optimal, STR-Net training is offline and not part of real-time control, and no code release is mentioned.