Experimental evaluation of various task-space control algorithms shows that significant deviations from desired trajectories may occur, especially at higher speeds, or in the vicinity of singularities. The experiments on a modular reconfigurable robotic setup confirmed this conclusion: the lateral deviations may range up to several centimeters from the closest point on the desired trajectory. The main reason is that the control output often reaches the saturation value of an actuator. The lateral error is also found very dangerous in obstacle cluttered environments due to possible damage of the manipulator arm while hitting an obstacle at high speed. This paper is devoted to solve this problem. Widely used task space control algorithms such as the resolved-rate and the resolved-acceleration algorithms are modified by introducing monitoring on the control output, and, accordingly, modifying the commanded control signal so that the end-effector is prevented from leaving the programmed path. As a consequence, the manipulator tip may slowdown along the path due to limited actuator power, but it will be accelerated after that to reach the desired position as soon as possible. The algorithms also take into account the presence of singularities to avoid uncontrollable excursions of the manipulator tip. Hundreds of experiments have been carried out to confirm the concept. Some of those with a desired trajectory reaching both the regular and the singular region of the workspace are provided to illustrate the method.

Robot operation near isotropic configurations, where the condition number of its Jacobian matrix reaches unity, is desirable from several points of view. However, determination of all such configurations, given an arbitrary robot geometry is rather a complex problem. In this paper all the isotropic configurations of planar manipulators with 2 and 3 degrees of freedom are determined. The solutions are obtained in the form of a 4th order polynomial for the 3-DOF robot, yielding maximally 8 sets of solutions. The condition numbers are obtained as explicit analytical functions of joint coordinates and link lengths' ratios. The optimal lengths of the links are determined by minimizing the criterion that the condition number increases most slowly with joint angles in the vicinity of isotropic configurations.>

In this paper the application of the damped least-squares method to the resolved-acceleration control is experimentally examined on a 2-DOF planar manipulator In order to decrease the position error introduced by the damping, only small singular values are damped. The symbolical expressions of the singular value decomposition of the Jacobian matrix were utilized in order to decrease the computational burden. Position error along the work-space boundary was only 15% greater than along the trajectories inside the reachable workspace.>

One of the problems in real-time control of redundant manipulators is considerably increased computational complexity compared with nonredundant robots. An attempt is made to reduce computational complexity by combining analytical and pseudoinverse solutions. In this way the dimensions of the Jacobian are considerably reduced, yielding several times less computational complexity. Further reduction of computational time is achieved by applying the gradient projection method to the actually redundant subrobot. A simple performance criterion for avoiding wrist singularity is proposed.>

The authors address the problem of the optimal evaluation of robot inverse dynamics on array processors. The inverse dynamics models used are the symbolic customized models with near-minimum numerical complexity, which are computer-generated given the robot arm parameters. Such models represent the input for a proposed scheduling algorithm that distributes the computation of the model over several multipliers and adders. The scheduling algorithm is automatic and minimizes the number of microcycles. The algorithm was tested on several standard robots, and processor efficiency up to 84% was achieved. Experimental results on a 30 MFLOPS array processor showed that the inverse dynamics of a three-link PUMA-like robot requires 25.5 mu s. For a six-link robot, the computation of the inverse dynamics and the control law takes about 100 mu s on this processor. Thus, the control of high-speed robots could be achieved by attaching low-cost array processors (10 MFLOPS) to the control processor of the robot controller.>

The solution to the inverse manipulation problem for redundant manipulators has mostly been considered from a geometric-kinematic standpoint. A procedure for the inverse problem solution using the dynamic model of the manipulator and its actuators is developed. Nominal trajectories in the space of joint coordinates are generated so as to be optimal with respect to total energy consumption of the actuators (hydraulic or electric). The treatment of constraints on joint coordinates and rates is also involved in the procedure. The algorithm is illustrated by two industrial robots.