Whole-Body Safe Control of Robotic Systems with Koopman Neural Dynamics

TL;DR

This paper introduces a data-driven approach that combines Koopman operator theory with the Safe Set Algorithm to enable real-time, safe, and efficient control of complex robotic systems through a single quadratic program.

Contribution

It presents a novel framework that learns Koopman embeddings from data and integrates them with SSA for safe control, eliminating the need for separate safety filters.

Findings

Accurately tracks trajectories on Kinova Gen3 manipulator.

Enables obstacle avoidance on a quadruped robot.

Ensures safety and feasibility with a single quadratic program.

Abstract

Controlling robots with strongly nonlinear, high-dimensional dynamics remains challenging, as direct nonlinear optimization with safety constraints is often intractable in real time. The Koopman operator offers a way to represent nonlinear systems linearly in a lifted space, enabling the use of efficient linear control. We propose a data-driven framework that learns a Koopman embedding and operator from data, and integrates the resulting linear model with the Safe Set Algorithm (SSA). This allows the tracking and safety constraints to be solved in a single quadratic program (QP), ensuring feasibility and optimality without a separate safety filter. We validate the method on a Kinova Gen3 manipulator and a Go2 quadruped, showing accurate tracking and obstacle avoidance.