# EKMP: Generalized Imitation Learning with Adaptation, Nonlinear Hard Constraints and Obstacle Avoidance

arXiv: https://arxiv.org/abs/2103.00452 · HTML: https://mlsanity.com/paper/2103.00452/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 28 Feb 2021.

## Placed in

- Offline RL and imitation learning from data / [Robot learning from demonstration](https://mlsanity.com/offlinerl/robot-learning-from-demonstration/)

## Builds on (most cited first, 5 of 5)

- [Kernelized Movement Primitives](https://mlsanity.com/paper/1708.08638/) (2017)
- [Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems](https://mlsanity.com/paper/2003.11500/) (2020)
- [Uncertainty-Aware Imitation Learning using Kernelized Movement Primitives](https://mlsanity.com/paper/1903.02114/) (2019)
- [Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1601.03648/) (2016)
- [A Linearly Constrained Nonparametric Framework for Imitation Learning](https://mlsanity.com/paper/1909.07374/) (2019)

## Built on by (most cited first, 2 of 2)

- [Constrained Equation Learner Networks for Precision-Preserving Extrapolation of Robotic Skills](https://mlsanity.com/paper/2311.02475/) (2023)
- [Infeasible optimization problems and the hierarchical augmented Lagrangian method in imitation learning](https://mlsanity.com/paper/2606.00730/) (2026)

## Abstract (arXiv)

As a user-friendly and straightforward solution for robot trajectory generation, imitation learning has been viewed as a vital direction in the context of robot skill learning. In contrast to unconstrained imitation learning which ignores possible internal and external constraints arising from environments and robot kinematics/dynamics, recent works on constrained imitation learning allow for transferring human skills to unstructured scenarios, further enlarging the application domain of imitation learning. While various constraints have been studied, e.g., joint limits, obstacle avoidance and plane constraints, the problem of nonlinear hard constraints has not been well-addressed. In this paper, we propose extended kernelized movement primitives (EKMP) to cope with most of the key problems in imitation learning, including nonlinear hard constraints. Specifically, EKMP is capable of learning the probabilistic features of multiple demonstrations, adapting the learned skills towards arbitrary desired points in terms of joint position and velocity, avoiding obstacles at the level of robot links, as well as satisfying arbitrary linear and nonlinear, equality and inequality hard constraints. Besides, the connections between EKMP and state-of-the-art motion planning approaches are discussed. Several evaluations including the planning of joint trajectories for a 7-DoF robotic arm are provided to verify the effectiveness of our framework.