Defining Feasible Joint and Geometric Workspaces Through Boundary Functions

This work presents an alternative method for defining feasible joint-space boundaries and their corresponding geometric workspace in a planar robotic system. Instead of relying on traditional numerical approaches that require extensive sampling and collision detection, the proposed method constructs a continuous boundary by identifying key intersection points of boundary functions. The feasibility region is further refined through centroid-based scaling, addressing singularity issues and ensuring a structured trajectory. Comparative analyses demonstrate that the final robot pose and reachability depend on the selected traversal path, highlighting the nonlinear nature of the workspace. Additionally, an evaluation of traditional numerical methods reveals their limitations in generating continuous boundary trajectories. The proposed approach provides a structured method for defining feasible workspaces, improving trajectory planning in robotic systems.