An optimal visual servo trajectory planning method for manipulators based on system nondeterministic model

When a manipulator captures its target by a visual servo system, uncertainties can arise because of mechanical system and visual sensors exist error. This paper proposes an intelligent method to predict the successful rate for a manipulator to capture its target with motion and sensor errors. Because the mapping between the joint space of the manipulator and the Cartesian space at the end of the manipulator is nonlinear, when there is a bounded error of the manipulator's joint, the error range of the end motion is constantly changing with the different joint positions. And at the same time, the visual servo camera will also measure the target from different positions and postures, so as to produce measurement results with different error ranges. The unknown time-varying error property not only greatly affects the stability of the closed-loop control but also causes the capture failure. The purpose of this paper is to estimate the success probability of different capture trajectories by establishing the nondeterministic model of manipulator control system. First, a system model including motion subsystem and feedback subsystem was established with system error described by Gaussian probability. And then Bayesian estimation was introduced into the system model to estimate the executing state of the predefined trajectory. Linear least quadratic regulators (LQR) control is used to simulate the input correction in the closed-loop control between motion subsystem and feedback subsystem. At last, the successful probability of capturing the target is established by the Gaussian distribution at the end point of the trajectory with geometric relationship calculation between tolerance range and error distribution. The effectiveness and practicability of the proposed method are proved by simulation and experiment.