Kernelized Movement Primitives (1708.08638v2)

Abstract: Imitation learning has been studied widely as a convenient way to transfer human skills to robots. This learning approach is aimed at extracting relevant motion patterns from human demonstrations and subsequently applying these patterns to different situations. Despite many advancements have been achieved, the solutions for coping with unpredicted situations (e.g., obstacles and external perturbations) and high-dimensional inputs are still largely open. In this paper, we propose a novel kernelized movement primitive (KMP), which allows the robot to adapt the learned motor skills and fulfill a variety of additional constraints arising over the course of a task. Specifically, KMP is capable of learning trajectories associated with high-dimensional inputs due to the kernel treatment, which in turn renders a model with fewer open parameters in contrast to methods that rely on basis functions. Moreover, we extend our approach by exploiting local trajectory representations in different coordinate systems that describe the task at hand, endowing KMP with reliable extrapolation capabilities in broader domains. We apply KMP to the learning of time-driven trajectories as a special case, where a compact parametric representation describing a trajectory and its first-order derivative is utilized. In order to verify the effectiveness of our method, several examples of trajectory modulations and extrapolations associated with time inputs, as well as trajectory adaptations with high-dimensional inputs are provided.

• The paper presents a novel kernel-based framework that models movement trajectories non-parametrically, enhancing robotic imitation learning.
• It minimizes the KL-divergence between predictive and reference distributions to effectively capture movement variability and uncertainty.
• The approach adapts to new constraints and high-dimensional inputs, ensuring scalable and robust performance in dynamic environments.

Kernelized Movement Primitives for Robotic Imitation Learning

The paper "Kernelized Movement Primitives" by Huang et al. presents a novel framework that addresses key challenges in imitation learning for robots, specifically in learning, adapting, and extrapolating movement trajectories from human demonstrations. At its core, this framework introduces Kernelized Movement Primitives (KMP), a methodology that leverages kernel-based learning to model motor skills without the need for explicit basis functions, thus mitigating issues related to high-dimensional input spaces and adapting to unforeseen task constraints such as obstacles or via-points.

Problem Context and Solution

The ability of robots to learn and adapt human-like movements is crucial in many automated and semi-automated tasks. Traditional methods like Dynamic Movement Primitives (DMP) and Probabilistic Movement Primitives (ProMP) involve explicit basis functions, which can lead to high parameterization and limit scalability when dealing with high-dimensional data. KMP addresses these limitations by representing trajectories in a non-parametric manner, using kernel functions to implicitly define the movement space, reducing the need for large open parameter sets.

Numerical Highlights:

KMP demonstrates the capability to:

• Adapt trajectories to a variety of newly imposed constraints (such as via-points or changes in goal positions).
• Handle high-dimensional input spaces more effectively compared to methods relying on fixed basis functions.
• Provide probabilistic prediction that includes mean and covariance estimates, allowing for modeling trajectory distributions and capturing variability in demonstrations efficiently.

Key Contributions and Theoretical Implications

1. Kernelization of Movement Primitives: KMP employs kernel functions to implicitly model the feature space. This kernelization is crucial for handling high-dimensional inputs, a significant advancement over methods like DMP and ProMP which require explicit basis functions.
2. Information-Theoretic Optimization: The movement learning in KMP is positioned as an optimization problem where the Kullback-Leibler divergence (KL-divergence) between the predictive and reference trajectory distributions is minimized. This ensures that the robot’s generated trajectory closely matches the variety and uncertainty of human demonstrations.
3. Adaptive and Generalizable Movement: The paper extends KMP to handle new trajectory constraints and task parameterizations, such as via local coordinate systems, that facilitate not only adaptation but also reliable extrapolation of learned behaviors to new situations.

Implications of KMP:

Practically, KMP enhances the adaptability of robots in dynamic and unstructured environments, making it possible for a robot to react effectively to unforeseen events during task execution. Theoretically, it challenges the traditional reliance on fixed basis functions and linear representations in trajectory learning, pushing the field towards more flexible and scalable solutions.

Speculation on Future Developments in AI

Advancing the principles set out in KMP could lead to breakthroughs in more generalized learning frameworks for robots. Potential future directions include:

• Integration with Reinforcement Learning: Combining KMP with reinforcement learning strategies to autonomously refine trajectory adaptations without explicit human interventions.
• Scalability in Collaborative Multi-Robot Systems: Extending the framework to coordinate movements within teams of robots, optimizing group dynamics in tasks such as cooperative manipulation or swarm robotics.
• Human-Robot Interfaces: Using KMP as a foundation for developing intuitive control interfaces, allowing non-expert users to teach robots new tasks through natural interactions.

In summary, the paper introduces a robust movement primitive framework that elegantly combines kernel-based learning with imitation learning principles, offering a promising path for developing adaptable and efficient robotic systems capable of mirroring complex human movements.