Hierarchical Proportion Models for Motion Generation via Integration of Motion Primitives

Imitation learning (IL) enables robots to acquire human-like motion skills from demonstrations, but it still requires extensive high-quality data and retraining to handle complex or long-horizon tasks. To improve data efficiency and adaptability, this study proposes a hierarchical IL framework that integrates motion primitives with proportion-based motion synthesis. The proposed method employs a two-layer architecture, where the upper layer performs long-term planning, while a set of lower-layer models learn individual motion primitives, which are combined according to specific proportions. Three model variants are introduced to explore different trade-offs between learning flexibility, computational cost, and adaptability: a learning-based proportion model, a sampling-based proportion model, and a playback-based proportion model, which differ in how the proportions are determined and whether the upper layer is trainable. Through real-robot pick-and-place experiments, the proposed models successfully generated complex motions not included in the primitive set. The sampling-based and playback-based proportion models achieved more stable and adaptable motion generation than the standard hierarchical model, demonstrating the effectiveness of proportion-based motion integration for practical robot learning.

💡 Research Summary

Imitation learning (IL) enables robots to acquire human‑like motion skills from demonstrations, but it suffers from high data demand and the need for repeated retraining when faced with complex or long‑horizon tasks. To address these limitations, the authors propose a hierarchical IL framework that combines reusable motion primitives with proportion‑based synthesis. The architecture consists of two layers. The lower layer contains multiple expert models (implemented as multilayer perceptrons) that each learn a short‑duration motion primitive. Primitives are extracted automatically by uniformly segmenting demonstration trajectories in time, rather than by task‑specific semantic labeling, which enhances generalization. The upper layer is responsible for long‑term planning and for determining how the primitive outputs should be combined. Three variants of the proportion‑determination mechanism are explored.

1. Learning‑based proportion model – The upper layer is an LSTM network that simultaneously learns long‑term planning and the softmax‑normalized mixing coefficients for the primitives. The weighted average of the lower‑layer outputs yields the command for the next time step.

2. Sampling‑based proportion model – Inspired by Monte‑Carlo Model Predictive Control (MC‑MPC), the upper layer predicts future follower states. The lower layer then generates leader trajectories conditioned on these predictions, adding stochastic noise to create a large set of candidate samples. Each sample is evaluated with a cost function that aggregates mean‑squared errors of joint angles, velocities, and torques. Using the cross‑entropy method, the top‑performing samples receive higher weights, and a weighted average produces the final command. This approach does not require explicit learning of mixing coefficients; the sampling process implicitly determines the proportions.

3. Playback‑based proportion model – The upper layer is replaced by pre‑collected motion data that serve as the target trajectory. The lower‑layer models still generate noisy samples, which are evaluated against the recorded data using the same cost function as in the sampling‑based model. Because the upper layer is fixed, no retraining is needed when new tasks are introduced, dramatically reducing adaptation time and overall learning cost.

The framework was validated on a real‑robot pick‑and‑place platform. Fifty primitives were collected from five directional motions (left‑to‑right, right‑to‑left, front‑to‑back, etc.) and segmented into ten overlapping time windows each. Two test tasks were used: (i) a simple right‑to‑left motion already present in the primitive set, and (ii) a more complex two‑object transfer task that was not represented among the primitives. Objects with varying shape and stiffness were employed during execution to assess robustness to environmental changes.

Experimental results show that all three proposed models can synthesize the complex two‑object task by recombining existing primitives, demonstrating the feasibility of generating unseen motions without additional task‑specific data. The learning‑based model struggled when many primitives were involved, leading to inaccurate proportion estimates and higher trajectory errors. In contrast, both the sampling‑based and playback‑based models achieved lower mean‑squared errors, smoother transitions, and greater stability across different object properties. Moreover, because the lower‑layer primitives are shared across tasks, the overall training burden is reduced; the playback‑based variant further eliminates the need for any upper‑layer training, enabling rapid deployment in new scenarios.

In summary, this work introduces a novel hierarchical structure that merges the strengths of Mixture‑of‑Experts and MC‑MPC, applying it to real‑world robot motion generation. By decoupling primitive learning from proportion determination, the approach improves data efficiency, facilitates reuse of motion modules, and offers flexible adaptation mechanisms for complex, long‑horizon robotic tasks.