# Kernelized Movement Primitives

arXiv: https://arxiv.org/abs/1708.08638 · HTML: https://mlsanity.com/paper/1708.08638/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Aug 2017.

## Built on by (most cited first, 30 of 37)

- [Learning Riemannian Manifolds for Geodesic Motion Skills](https://mlsanity.com/paper/2106.04315/) (2021)
- [Interactive Imitation Learning of Bimanual Movement Primitives](https://mlsanity.com/paper/2210.16220/) (2022)
- [Hierarchical Neural Dynamic Policies](https://mlsanity.com/paper/2107.05627/) (2021)
- [A Survey on Imitation Learning for Contact-Rich Tasks in Robotics](https://mlsanity.com/paper/2506.13498/) (2025)
- [Learning Stable Vector Fields on Lie Groups](https://mlsanity.com/paper/2110.11774/) (2021)
- [Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives](https://mlsanity.com/paper/1903.02114/) (2019)
- [The Art of Imitation: Learning Long-Horizon Manipulation Tasks from Few Demonstrations](https://mlsanity.com/paper/2407.13432/) (2024)
- [Orientation Probabilistic Movement Primitives on Riemannian Manifolds](https://mlsanity.com/paper/2110.15036/) (2021)
- [Bayesian Disturbance Injection: Robust Imitation Learning of Flexible Policies for Robot Manipulation](https://mlsanity.com/paper/2211.03393/) (2022)
- [Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policies](https://mlsanity.com/paper/2305.10411/) (2023)
- [Benchmark for Skill Learning from Demonstration: Impact of User Experience, Task Complexity, and Start Configuration on Performance](https://mlsanity.com/paper/1911.02725/) (2019)
- [Learning from demonstration with model-based Gaussian process](https://mlsanity.com/paper/1910.05005/) (2019)
- [Bayesian Disturbance Injection: Robust Imitation Learning of Flexible Policies](https://mlsanity.com/paper/2103.13623/) (2021)
- [Reactive Motion Generation on Learned Riemannian Manifolds](https://mlsanity.com/paper/2203.07761/) (2022)
- [Gaussian-Process-based Robot Learning from Demonstration](https://mlsanity.com/paper/2002.09979/) (2020)
- [MMP++: Motion Manifold Primitives with Parametric Curve Models](https://mlsanity.com/paper/2310.17072/) (2023)
- [Interactive incremental learning of generalizable skills with local trajectory modulation](https://mlsanity.com/paper/2409.05655/) (2024)
- [A Linearly Constrained Nonparametric Framework for Imitation Learning](https://mlsanity.com/paper/1909.07374/) (2019)
- [The Unreasonable Effectiveness of Discrete-Time Gaussian Process Mixtures for Robot Policy Learning](https://mlsanity.com/paper/2505.03296/) (2025)
- [EKMP: Generalized Imitation Learning with Adaptation, Nonlinear Hard Constraints and Obstacle Avoidance](https://mlsanity.com/paper/2103.00452/) (2021)
- [Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series](https://mlsanity.com/paper/2104.10731/) (2021)
- [Similarity-Aware Skill Reproduction based on Multi-Representational Learning from Demonstration](https://mlsanity.com/paper/2110.14817/) (2021)
- [Task-Adaptive Robot Learning from Demonstration with Gaussian Process Models under Replication](https://mlsanity.com/paper/2010.07795/) (2020)
- [A Structured Prediction Approach for Robot Imitation Learning](https://mlsanity.com/paper/2309.14829/) (2023)
- [Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations](https://mlsanity.com/paper/2504.18860/) (2025)
- [IROSA: Interactive Robot Skill Adaptation using Natural Language](https://mlsanity.com/paper/2603.03897/) (2026)
- [Implicit Drifting Policy: One-Step Action Generation via Conditional Expert Geometry](https://mlsanity.com/paper/2606.01098/) (2026)
- [A Non-parametric Skill Representation with Soft Null Space Projectors for Fast Generalization](https://mlsanity.com/paper/2209.08522/) (2022)
- [Auto-LfD: Towards Closing the Loop for Learning from Demonstrations](https://mlsanity.com/paper/2310.09791/) (2023)
- [Non-parametric regression for robot learning on manifolds](https://mlsanity.com/paper/2310.19561/) (2023)

## Abstract (arXiv)

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.