Numerical method for obtaining the inverse kinematics of six-degree-of-freedom serial robot with an offset wrist

A numerical method for obtaining the inverse kinematics of a six-degree-of-freedom serial robot with an offset wrist, comprising the following steps:

• A. use the pose of the terminal coordinate frame of the six-degree-of-freedom serial robot with an offset wrist as the pose of the terminal coordinate frame of a six-degree-of-freedom serial robot with a non-offset wrist to obtain an analytical solution θ′1˜θ′6 of the inverse kinematics of the six-degree-of-freedom serial robot with a non-offset wrist;
• B. use the analytical solution θ1′˜θ6′ as an approximate solution of the inverse kinematics of the six-degree-of-freedom serial robot with an offset wrist and an initial point for iterative calculation using an iteration method;
• use θ1′˜θ6′ to obtain the approximate pose of the terminal coordinate frame according to a formula for obtaining the forward kinematics of the six-degree-of-freedom serial robot with an offset wrist;
• C. obtain a pose increment dX of the expected pose of the terminal coordinate frame with respect to the approximate pose of the terminal coordinate frame through calculation, and obtain the synthetic error e of the pose of the terminal coordinate frame by using dX;
• D. judge whether the synthetic error e is within a reasonable error range or not;
• if the synthetic error is within the reasonable error range, stop and return the current numerical solution of the joint variable as an iterative numerical solution of the inverse kinematics of the six-degree-of-freedom serial robot with an offset wrist;
• if the synthetic error e is not within the reasonable error range, obtain the joint variable θ′ through a jacobian matrix of the six-degree-of-freedom serial robot with an offset wrist, and put the new joint variable θ′ into step B and step C to conduct iterative calculation until the synthetic error e is within the reasonable error range or the maximum number of iterations is reached and then return a current numerical solution of the joint variable as the iterative numerical solution of the inverse kinematics of the six-degree-of-freedom serial robot with an offset wrist.