A Method for Manipulator Motion Planning Based on Constructing Graphs of Convex Sets via Gaussian Mixture Models

Abstract

Motion planning for redundant manipulators in high-dimensional configuration spaces, while simultaneously handling complex obstacles and multiple motion performance constraints, remains a challenge. In this article, a motion planning method for manipulators based on a Graphs of Convex Sets constructed via Gaussian Mixture Models (GMM-GCS) is proposed. The free configuration space is approximated by multiple convex sets represented by Gaussian components. These convex sets are further optimized through convex set selection and adjustment, and the remaining convex sets together with their intersection regions are used to construct the Graphs of Convex Sets (GCS). A comprehensive performance index is introduced during the training of Gaussian Mixture Models (GMM) to incorporate motion performance into the GMM-GCS model. A projection-based method is developed to reliably identify both direct and wormhole connections between convex sets in high-dimensional spaces. Motion planning is then performed on the constructed GCS using Dijkstra’s algorithm, followed by path optimization based on the joint probability density of the GMM. Simulation and real-world experiments on 3-DOF, 7-DOF, and 12-DOF manipulators show that the proposed method achieves improved planning efficiency and motion performance over other methods in complex scenarios. Note to Practitioners—This article addresses a practical problem of motion planning for redundant manipulators operated in complex obstacle scenarios, where high-dimensional configuration spaces and multiple motion performance requirements make planning computationally demanding. In real-world applications such as assembly and material handling, planners must not only generate collision-free paths but also ensure desirable motion quality, including smoothness and kinematic feasibility. Traditional methods often struggle to balance efficiency and performance in such scenarios. The proposed GMM-GCS framework approximates the free configuration space using convex sets and organizes them into a GCS for efficient global planning. By incorporating a comprehensive performance index into the modeling process, motion quality is directly considered during space construction. This makes the approach suitable for manipulators with different degrees of freedom in structured scenarios. However, the method relies on prior modeling of the workspace and may require additional updates in highly dynamic settings. Future improvements could focus on adaptive model refinement for changing scenarios.