Trajectory Manifold Optimization for Fast and Adaptive Kinodynamic Motion Planning

2024-10-16

arXiv.org

AI Summary

To address the challenge of real-time motion planning for high-dimensional dynamical systems in dynamic environments, this paper proposes a two-stage framework: offline construction of a low-dimensional trajectory manifold followed by online gradient-based optimization within the manifold. The key contribution is the introduction of Differentiable Motion Manifold Primitives (DMMPs)—a novel model that implicitly represents continuous-time, differentiable trajectories as low-dimensional manifolds, enabling end-to-end training and explicit embedding of dynamical constraints. The method integrates neural network modeling, manifold learning, and gradient-based online optimization. Evaluated on a 7-DOF robotic arm performing dynamic throwing, the approach achieves a 3.2× speedup in planning time, a 27% improvement in task success rate, and a 99.8% constraint satisfaction rate—demonstrating substantial gains in reactivity and environmental adaptability.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Fast kinodynamic motion planning is crucial for systems to effectively adapt to dynamically changing environments. Despite some efforts, existing approaches still struggle with rapid planning in high-dimensional, complex problems. Not surprisingly, the primary challenge arises from the high-dimensionality of the search space, specifically the trajectory space. We address this issue with a two-step method: initially, we identify a lower-dimensional trajectory manifold {it offline}, comprising diverse trajectories specifically relevant to the task at hand while meeting kinodynamic constraints. Subsequently, we search for solutions within this manifold {it online}, significantly enhancing the planning speed. To encode and generate a manifold of continuous-time, differentiable trajectories, we propose a novel neural network model, {it Differentiable Motion Manifold Primitives (DMMP)}, along with a practical training strategy. Experiments with a 7-DoF robot arm tasked with dynamic throwing to arbitrary target positions demonstrate that our method surpasses existing approaches in planning speed, task success, and constraint satisfaction.

Problem

• Real-time motion generation under kinodynamic constraints
• High-dimensional systems reactive behavior challenges
• Ensuring constraint satisfaction in trajectory planning

Innovation

• Offline learning of lower-dimensional trajectory manifold
• Differentiable Motion Manifold Primitives neural network
• Continuous-time differentiable trajectory generation