Consistent Solution Strategy for Static Equilibrium Workspace and Trajectory Planning of Under-Constrained Cable-Driven Parallel and Planar Hybrid Robots

This paper presents a consistent solution strategy for static equilibrium workspaces of different types of under-constrained robots. Considering the constraint conditions of cable force and taking the least squares error of the static equilibrium equation as the objective, the convex optimization solution is carried out, and the static equilibrium working space of the under-constrained system is obtained. A consistent solution strategy is applied to solve the static equilibrium workspaces of the cable-driven parallel and planar hybrid robots. The dynamic models are presented and introducing parameters that are applied to make the system stable for point-to-point movements. Based on this model, the traditional polynomial-based point-to-point trajectory planning algorithm is improved by adding unconstrained parameters to the kinematic law function. The constraints of the dynamics model are incorporated into the trajectory planning process to achieve point-to-point trajectory planning for the under-constrained cable-driven robots. Finally, under-constrained cable-driven parallel robots with three cables and planar hybrid robot with two cables are taken as examples to carry out numerical simulation. The final results show that the point-to-point trajectory planning algorithm introducing parameters is effective and feasible and can provide theoretical guidance for the design of subsequent under-constrained robots.