A simple nonlinear proportional-integral-derivative (PID) controller is proposed for global finite-time regulation of robot manipulators without velocity measurements. A Lyapunov-based stability argument is employ to prove global finite-time stabilization. The proposed control algorithm does not involve the model parameters in the control law formulation and the control gains can be explicitly determined based on some well-known bounds extracted from the robot dynamics, and thus permits easy implementation. Simulations are included to demonstrate the expected properties of the proposed approach.

A simple nonlinear proportional-integral-derivative (PID) controller is proposed to solve the finite-time regulation of uncertain robot manipulators. The semiglobal finite-time stabilization is shown by using Lyapunov theory and finite-time stability theory. The proposed control algorithm does not involve the modeling information in the control law formulation and the control gains can be explicitly determined based on some well-known bounds extracted from the robot dynamics, and thus permits easy implementation. Simulations preformed on a two degrees-of-freedom (DOF) manipulator demonstrate the expected properties of the proposed approach.

A simple continuous output feedback proportional-derivative (PD) plus desired gravity compensation controller is proposed to solve the global finite-time regulation of robot manipulators with position measurements only. The global finite-time convergence is proved by using Lyapunov theory and finite-time stability theory. Simulations preformed on a two degrees-of-freedom (DOF) manipulator demonstrate the expected properties of the proposed approach.

In this paper, we provide an answer to the long-standing question of designing global asymptotically stable proportional-integral-derivative (PID) regulators with only position feedback for uncertain robots. Our main contribution is to establish the global asymptotic stability of the controlled system by using Lyapunov direct method and LaSalle's invariance principle. We provide explicit conditions on the regulator gains to ensure global asymptotic stability. The proposed controller does not utilize the modeling information in the control formulation, and thus permits easy implementation. Simulations performed on a planar two degrees-of-freedom robot manipulator demonstrate the effectiveness of the proposed approach.

High-quality low speed motion control calls for precise position and velocity signals. However, velocity estimation based on simple numerical differentiation from the only position measurement may be very erroneous, especially in the low-speed regions. A simple linear velocity estimator is proposed based for high-quality instantaneous velocity estimation, on position measurements only. The proposed estimator is constructed based on the fact that velocity belongs to the chain of kinematic quantities: position and velocity, and numerical integration can provide more stable and accurate results than numerical differentiation in the presence of noise. The main attraction of the new algorithm is that it is very effective as well as in low-speed ranges, high robustness against noise, and easy to implement with simple computation. Both extensive simulations and experimental tests have been performed to verify the effectiveness and efficiency of the proposed approach.

A new singularity analysis method for a general 6 degree-of-freedom (DOF) Stewart platform using genetic algorithm (GA) is proposed in the paper. The Jacobian matrix of the Stewart platform is first deduced, then the square of determinant of the Jacobian matrix is selected as the objective function, and the minimum of this objective function is searched in the workspace of the Stewart platform by a real-coded GA. The singularity of the Stewart platform depends on this minimum objective function, if this value is zero, the singularity of Stewart platform will happen, otherwise, the Stewart platform is singularity-free. The effectiveness of this new genetic singularity analysis method is validated by numerical simulation.