Parallel robots control the movement of their end-effector or gripper through multiple kinematic chains connected in parallel, forming closed kinematic chains. This provides them with greater structural rigidity and dynamic performance, but it also limits their workspace and divides it into different regions separated by parallel-type singularities (also known as type 2 singularities) that do not exist in serial or open kinematic chain robots. When the robot crosses one of these singularities, it is not possible to control the movement of its end-effector in any arbitrary direction, requiring infinitely large actuation torques in the actuators. This makes it difficult to cross such singularities to fully utilize the robot's workspace.

In previous works, other researchers have avoided the divergence of actuation torques by designing the end-effector's trajectory so that, when crossing the singularity, the robot's dynamic model does not degenerate, satisfying a non-degeneration condition derived by other researchers in the past. The drawback is that the trajectory used to cross the singularity cannot be arbitrary; it must be designed to meet the mentioned non-degeneration condition.

In this project, we propose the design of new Computed-Torque Control laws that allow crossing the mentioned parallel singularities while avoiding the divergence of the actuation torques, so that they remain finite during the crossing of the singularity, and additionally avoiding the need to design the trajectory to achieve this, thus allowing arbitrary trajectories. To achieve this in the present project, we propose considering the small modeling errors that always occur when modeling the dynamics of the robot to be controlled. These small errors cause the tracking of the desired trajectory to be imperfect, which provides some margin to meet the non-degeneration condition simply by adjusting the proportional and derivative gains of the regulator, leaving the trajectory completely free. The proposed control will be tested in this project through simulation with example parallel robots, and also through testing on real parallel robots.

Project funded by the Department of Innovation, Universities, Science, and Digital Society of the Generalitat Valenciana.