Stability and periodic solution on a robot trajectory generation model

Robot motion planning is an important topic, which is widely studied. In this paper, a neural network model, which is inspired biologically to construct the robot trajectory, is discussed. Both global exponential stability and periodic solutions of the neural network, which are also two of the most important characters of a dynamic system, are analyzed via the method of constructing suitable Lyapunov functions. Simple sufficient conditions are given for exponential stability and the existence of periodic solutions. The conditions in the results are presented in terms of the parameters of the connection matrix, which are easy to be checked and are helpful in practice.