A Parameter-Linear Formulation of the Optimal Path Following Problem for Robotic Manipulator

2025-10-23

AI Summary

Time-optimal path tracking for robotic manipulators suffers from singularities and low computational efficiency when the path velocity reaches zero. Method: This paper proposes a path-parameterization-based optimization method that maximizes the path velocity—distinct from conventional total-time minimization frameworks—thereby inherently avoiding zero-velocity singularities while embedding trajectory smoothness and dynamic feasibility into the objective. The original nonlinear optimization problem is reformulated via discretization into a linearly parameterized form, enabling efficient and numerically stable solution via linear programming. Contribution/Results: Experiments demonstrate that the proposed method significantly reduces computational cost while generating time-optimal trajectories that are singularity-free and highly smooth, thereby enhancing real-time performance and robustness of path tracking.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Motion and Path Planning
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Tracking, profiling, and countermeasures against them

Abstract

In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization problem in terms of a path parameter. Thus, smooth trajectory generation while maintaining a low computational effort is quite challenging, since the singularities have to be taken into account. To this end, a different approach is presented in this paper. This approach is based on maximizing the path speed along a prescribed path. Furthermore, the approach is capable of planning smooth trajectories numerically efficient. Moreover, the discrete reformulation of the underlying problem is linear in optimization variables.

Problem

• Addressing computational challenges in time-optimal robotic path following
• Maximizing path speed along prescribed paths for smooth trajectories
• Developing linear discrete formulations for efficient numerical optimization

Innovation

• Maximizing path speed along prescribed path
• Planning smooth trajectories numerically efficient
• Discrete reformulation linear in optimization variables