Trajectory Planning for Parallel Robots in Dynamic Environments Using Precomputed Configuration Space Constraints

Trajectory planning for parallel manipulators in dynamic environments entails high computational costs, as geometric collision checks must be repeated whenever the environment changes. This paper proposes a trajectory planning method that shifts the most resource-intensive geometric constraint processing operations from the real-time planning stage to a preprocessing stage; this is achieved by precomputing constraints in the generalized coordinate space. To this end, a discrete mapping is established between safe-zone cells in the workspace and the discretized generalized coordinate space. An incremental constraint update mechanism, utilizing an aggregated conflict counter, allows for the incorporation of dynamic obstacle information without requiring repeated geometric analysis. Trajectory optimization is performed in the generalized coordinate space using a genetic algorithm, followed by temporal parameterization that accounts for actuator speed limits. Simulation results demonstrate the method’s efficiency in trajectory replanning amidst changing obstacle configurations, while experimental validation on a Delta robot confirms its practical applicability. Under the experimental conditions examined, the proposed method required approximately 1 s in total for initial planning and two replanning steps, whereas RRT and RRTX algorithms required approximately 5 s and 3.91 s, respectively; furthermore, the proposed method yielded the best objective function value for the final trajectory.