Optimization And Control Of Manipulability Of Robot Visual Servo Trajectory

Robot manipulability optimization is an inevitable problem in robot control.When the manipulability is poor,the robot's ability of freely moving in some directions decreases sharply.When a robot performs visual servo,the Jacobian matrix of the robot with poor manipulability is ill-conditioned.At this time,the joints of the robot is easy to overspeed and thus damage the joint.Therefore,it is necessary to improve the manipulability of the robot in motion.In this paper,a trajectory optimization method based on potential field method is studied to optimize the trajectory in real time in order to make the robot move in a highly flexible direction.In order to ensure the real-time performance of trajectory optimization,this paper presents the singular value approximation theorem of Jacobian matrix for robots,and proposes the singular value approximation algorithm and the fast flexibility gradient algorithm to reduce the computational complexity and improve the computational speed.In chapter two and three,the robot and visual servo system are modeled.Firstly,the DH model is used to establish the kinematics model of the robot.Then two common methods to calculate the Jacobian matrix of the robot are given.The relationship between the differential transformation method and the vector product method of the Jacobian matrix of the robot is analyzed.Secondly,this paper analyses the camera model,deduces the image Jacobian matrix,and proposes a depth-independent image Jacobian matrix for high-level image features.Finally,the visual servo system is analyzed in detail,in which the kinematics control model of visual servo is proposed,and the controller is designed to control the highly non-linear system.In Chapter four,this paper mainly discusses the singular value approximation theorem of Jacobian matrix for robots.The result of singular value decomposition and the derivability and continuity of the singular value show that the singular value changes continuously with the continuous change of the matrix elements,which reveals that the singular value of Jacobian matrix of a robot changes continuously with the motion of the robot.Therefore,the singular value decomposition information of the previous moment can be used to obtain the current singular value.The singular value approximation theorem of Jacobian matrix is proposed and the singular value approximation algorithm is given based on this property.In the fifth chapter of this paper,the trajectory optimization method based on potential field is proposed.This paper constructed the trajectory optimization potential field for kinematic control scheme and visual servo.In order to accelerate the calculation speed of potential field force,thisp aper studies the existence of robot manipulability gradient,and presents a fast manipulability gradient calculation algorithm to reduce the computation time.Experiments in chapter six of this paper prove the effectiveness of the theorem and algorithm proposed in this paper.The singular value approximation theorem can reduce the time-consuming of singular value calculation while guaranteeing certain accuracy.Fast manipulability gradient algorithm can also reduce computational complexity compared with ordinary numerical differentiation.The simulation and practical experiments verify the effectiveness of the potential field for trajectory optimization of the robot.