This study focuses on the accurate tracking control and sensorless estimation of external force disturbances on robot manipulators. The proposed approach is based on an adaptive Wavelet Neural Network (WNN), named Adaptive Force-Environment Estimator (WNN-AFEE). Unlike disturbance observers, WNN_AFEE does not require the inverse of the Jacobian transpose for computing the force, thus, it has no computational problem near singular points. In this scheme, WNN estimates the external force disturbance to attenuate its effects on the control system performance by estimating the environment model. A Lyapunov based design is presented to determine adaptive laws for tuning WNN parameters. Another advantage of the proposed approach is that it can estimate the force even when there are some parametric uncertainties in the robot model, because an additional adaptive law is designed to estimate the robot parameters. In a theorem, the stability of the closed loop system is proved and a general condition is presented for identifying the force and robot parameters. Some suggestions are provided for improving the estimation and control performance. Then, a WNN-AFEE is designed for a planar manipulator as an example, and some simulations are performed for different conditions. WNN_AFEE results are compared attentively with the results of an adaptive force estimator and a disturbance estimator. These comparisons show the efficiency of the proposed controller in dealing with different conditions. 
Adaptive force–environment estimator for manipulators based on adaptive wavelet neural network