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To solve the seam tracking problem of the mobile welding robot, a prototype of mobile welding robot with welding torch positioned at one side of welding robot is developed. And a new controller based on the dynamics of the mobile welding robot was designed. To make the tracking more quickly and smoothly, the controller combined the algorithm of the integral backstepping and the algorithm of the nerve network as its control algorithm, and utilized the self-learning neural network to deal with the partial uncertainty and the disturbances of the parameters of the robot model. It is proved that the selected control input torques make the system globally asymptotically stable based on the Lyapunov function selected out. Finally, the effectiveness of the controller is demonstrated by simulation results.