Admittance Controller Complemented with Real-time Singularity Avoidance for Rehabilitation Parallel Robots

Rehabilitation tasks demand robust and accurate trajectory-tracking performance, mainly achieved with parallel robots. In this field, limiting the value of the force exerted on the patient is crucial, especially when an injured limb is involved. In human-robot interaction studies, the admittance controller modifies the location of the robot according to the user efforts driving the end-effector to an arbitrary location within the workspace. However, a parallel robot has singularities within the workspace, making implementing a conventional admittance controller unsafe. Thus, this study proposes an admittance controller that overcomes the limitations of singular configurations by using a real-time singularity avoidance algorithm. The singularity avoidance algorithm modifies the original trajectory based on the actual location of the parallel robot. The complemented admittance controller is applied to a 4 degrees of freedom parallel robot for knee rehabilitation. In this case, the actual location is measured by a 3D tracking system because the location calculated by the forward kinematics is inaccurate in the vicinity of a singularity. The experimental results verify the effectiveness of the proposed admittance controller for safe knee rehabilitation exercises

A Type II Singularity Avoidance Algorithm for Parallel Manipulators using Output Twist Screws

Parallel robots (PRs) are closed-chain manipulators with diverse applications due to their accuracy and high payload. However, there are configurations within the workspace named Type II singularities where the PRs lose control of the end-effector movements. Type II singularities are a problem for applications where complete control of the end-effector is essential. Trajectory planning produces accurate movements of a PR by avoiding Type II singularities. Generally, singularity avoidance is achieved by optimising a geometrical path with a velocity profile considering singular configurations as obstacles. This research presents an algorithm that avoids Type II singularities by modifying the trajectory of a subset of the actuators. The subset of actuators represents the limbs responsible for a Type II singularity, and they are identified by the angle between two Output Twist Screws. The proposed avoidance algorithm does not require optimisation procedures, which reduces the computational cost for offline trajectory planning and makes it suitable for online trajectory planning. The avoidance algorithm is implemented in offline trajectory planning for a pick and place planar PR and a spatial knee rehabilitation PR

Experimental Analysis of Type II Singularities and Assembly Change Points in a 3UPS+RPU Parallel Robot

Parallel robots (PRs) have singular configurations where the robot gains at least one degree of freedom and loses control. Theoretically, such singularity occurs when the Forward Jacobian-matrix determinant becomes zero (Type II). However, actual PRs could lose control owing to Type II singularities for determinant values near zero, but not zero, because manufacturing tolerances introduce errors that are complex to model due to their low repeatability. Thus, using an actual 3UPS+RPU PR, this paper presents three contributions: i) a proximity detection index for Type II singularities based on the angle between two Output Twist Screws. The index can identify which kinematic chains contribute to the singularity. ii) an experimental benchmark to study Type II singularities. iii) PR configurations where the proposed index is zero and the Forward Jacobian determinant is not. In this last configuration, the findings show that the actual robot is unable to handle external actions applied to the PR.