[Paper Review] EKMP: Generalized Imitation Learning with Adaptation, Nonlinear Hard Constraints and Obstacle Avoidance

Yanlong Huang|arXiv (Cornell University)|Feb 28, 2021

Robot Manipulation and Learning23 references4 citations

TL;DR

This paper proposes Extended Kernelized Movement Primitives (EKMP), a generalized imitation learning framework that enables robots to learn from demonstrations while adapting to new goals, avoiding obstacles via link-level collision detection, and strictly satisfying both linear and nonlinear hard constraints—demonstrated effectively on a 7-DoF robotic arm with fast convergence and constraint compliance.

ABSTRACT

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.

Motivation & Objective

• To address the gap in constrained imitation learning, particularly for nonlinear hard constraints, obstacle avoidance, and joint-velocity consistency.
• To extend kernelized movement primitives (KMP) to support adaptation to arbitrary desired joint positions and velocities.
• To integrate obstacle avoidance at the level of robot links, not just end-effector positions.
• To satisfy arbitrary linear and nonlinear equality and inequality constraints during trajectory optimization.
• To enable fast, constraint-compliant trajectory planning with minimal human intervention.

Proposed method

• EKMP models multiple demonstrations using a Gaussian Mixture Model (GMM) to extract probabilistic features of joint positions and velocities.
• It employs Gaussian Mixture Regression (GMR) to derive a reference trajectory from the GMM parameters.
• A constrained optimization framework is formulated using a cost function combining imitation learning, obstacle avoidance, and hard constraint penalties.
• The method enforces the derivative relationship between position and velocity via a kernel-based regularization term in the optimization.
• Nonlinear constraints are handled through a penalty-based formulation with a barrier function, allowing both equality and inequality constraints to be incorporated.
• The optimization is solved iteratively using sequential quadratic programming (SQP), with constraints enforced at selected key points to reduce computational load.

Experimental results

Research questions

• RQ1 Can a generalized imitation learning framework handle nonlinear hard constraints while maintaining trajectory smoothness and velocity consistency?
• RQ2 How effectively can EKMP adapt learned skills to new goal states without additional demonstrations?
• RQ3 To what extent does EKMP outperform vanilla KMP in obstacle avoidance and constraint satisfaction?
• RQ4 Can the integration of Cartesian-space constraints (e.g., end-effector height limits) accelerate the planning of collision-free joint trajectories?
• RQ5 How does the framework perform under real-world robotic constraints, such as joint limits and link-level collisions?

Key findings

• EKMP achieved fast convergence in trajectory optimization, with obstacle avoidance cost decreasing rapidly—demonstrated in under 10 iterations on a 7-DoF robotic arm.
• Under both desired point and end-effector height constraints (z ≥ 0.4 m), EKMP satisfied all constraints after 9 iterations, even on long 200-point trajectories.
• With only 3 iterations, EKMP achieved obstacle avoidance under desired point constraints alone, and just 1 iteration when end-effector height constraints were added.
• The derivative relationship between joint position and velocity was strictly preserved throughout optimization, as confirmed by trajectory plots.
• Vanilla KMP failed to avoid obstacles, while EKMP-generated trajectories successfully avoided collisions across all evaluated scenarios.
• The integration of Cartesian constraints significantly accelerated convergence, indicating that high-level constraints can guide efficient joint trajectory planning.