Hybrid System Design for Singularityless Task Level Robot Controllers

This paper presents a hybrid system approach in the design of a singularityless task level controller. To achieve a singularityless motion control in the neighborhood of singularity, the hybrid system approach is used to integrate the task level controller and joint level controller. First, a hybrid system model is developed for the singularityless task level controller. A Max-Plus dynamic model is used to integrate the discrete switching control and continuous motion control in the controller. Based on this model, a smooth trajectory and control command /or the hybrid system can be obtained. The Lyapunov theory was used to prove the stability of the singularityless controller. The new singularityless task level controller has been experimentally implemented and tested on a PUMA 560 robot manipulator. Experimental results have been employed to verify the theoretical conclusions, thus clearly demonstrating the advantages of the new task level control method. 1 I n t r o d u c t i o n A robot task is usually described in its task space. The direct implementation of a task level controller can provide significant application efficiency and flexibility to a robotic operation. It becomes even more important when robots are working coordinately with humans. The human intuition on a task is always represented in the task space. However, the major problem in the application of the task level controller is the existence of singularities. While approaching a singular point, the task level controller generates high joint torques, which result in instability or large errors in the task space. The task level controller is not only * Research Partially suppor ted under NSF Grant [IS-9796300 and IIS-9796287. 0 -7803 -5886 -4 /00 /$ 10 .00© 2000 IEEE 300 I 48824, USA invalid at the singular points, but also cause instability in certain neighborhood of the singular points. Therefore, a number of methods have been proposed to solve the problem. A general idea is to avoid singularities by reducing the torque applied to individual joints. The basic damped least squares(DLS) method [1] modifies the end-effector path in terms of velocity. The inverse or the psudoinverse of the Jacobian matrix used in the task level controller does not exists and results in unreasonable values at or near the singular points. Instead of exact motion resulting large torques, the DLS method provides approximate motion close to the desired Cartesian trajectory. S. Chiaverini et al [2] refined the basic DLS method to improve deviation errors from the desired path by varying damping factors. A variable feedback gain is then set to zero within the vicinity and interpolation is used to achieve a smooth solution of the feedback gain [2]. An alternate method was developed incorporate the dynamics poles of the system. M. Sampei et al. [3] proposed a time re-scale transformation method for designing a robot controller, which achieves slow poles in the vicinity of singularity and fast poles in regular area. B. Bishop et al.[6] proposed a switching control method for redundancy resolution of redundant robots. The damped velocity method was used to maximize the manipulability. Torques and joint velocities are limited in utilizing the redundancy of the robot. A variable feedback gain, appropriate adjusted damping factors and the time reparameterizing methods result in similar Cartesian error dynamics. By these methods, the system is still unstable at the singular points. Obviously, it is not acceptable for many applications. M. Kirdanshi et al. [7] theoretically proved that at the singular points, the resolved acceleration control of robots has unstable saddles.