Singularity Identification for Robotic Manipulators and its Application to Trajectory Planning

Abstract

This work develops a method for identifying the singularity-free joint space of various manipulator systems. The starting point is the challenge of on-orbit servicing missions with robotic manipulators, where trajectory planning plays a crucial role. Manipulator singularities pose a central challenge in trajectory planning, as they can lead to loss of mobility, high actuator demands, and numerical instabilities. The developed methodology is based on the analysis of the Jacobian matrix of the manipulator system. Instead of directly determining the singularities algebraically, which is particularly complex for systems with a free-floating base, the singularity-free regions of the joint space are approximated using polytopes. The corresponding optimization method builds on the approach from [9] and is further developed in this work to make it applicable to manipulator systems with varying degrees of freedom and both fixed and free-floating bases. The method is applied to a free-floating manipulator with four degrees of freedom, a fixed-base manipulator with six degrees of freedom, and a redundant fixed-base manipulator with seven degrees of freedom. The results are compared with the singularities of the respective systems known from the literature. Subsequently, the method is used to identify the singularity-free regions of the joint space of a manipulator with six degrees of freedom. The system is modeled with both a fixed and a free-floating base, and the results are compared. The results show that the approximated polytopes reliably represent the singularities and are also applicable to more complex systems. For free-floating systems, it was shown that the coupling between the manipulator and the base leads to a curvature of the singularity surfaces, which is also captured by the polytopes. In the second part of the work, an approach is presented in which the identified polytopes are integrated into the trajectory planning of a manipulator system. The polytopes are formulated as additional inequality constraints, ensuring that their adherence avoids singularities. This approach leads to more robust and safer trajectories. The work demonstrates that the developed methodology provides a flexible and effcient way to identify the singularity-free regions of the joint space of various manipulator systems. By integrating the polytopes into trajectory planning, singularities can be reliably avoided, increasing the safety and reliability of autonomous robotic systems in on-orbit servicing missions.