Inverse kinematics of 6-DOF hybrid manipulator for forest-fruit harvest based on screw theory

Abstract: A method for inverse kinematics analysis based on screw theory was presented in this paper, which can directly map the position and orientation of the working object to the joint variables of the manipulator with its application to a full inverse kinematics analysis of forest-fruit harvesting manipulator characterized by a hybrid kinematic structure, 2P4R. The solution of inverse kinematics modeling derived by screw theory was commonly realized by Paden-Kahan sub-problem method, which decomposes a full kinematics problem into sub-problem with obviously geometrical meaning through choosing appropriate point, usually, intersection of adjacent joint, such as wrist joint, to reduce the number of the variable quantity, and then close-form solution can be easily obtained. However, in practice, it is hard to gain the position of those points through measure because of their absence before end-effector actually moving to the desired position. And few researchers mentioned this issue in the relevant literature. In order to discuss this problem, firstly, a geometrical method was proposed for this issue to obtain the position of the required point, wrist joint, according to the orientation of end-effector and its geometric properties and geometric relationships through using the vector algebra method. Furthermore, a mapping between driving and driven join was gained in order to simplify the solving process of the equation set at a later, according to the solution of the structural equation of the manipulator derived by the product-of-exponentials (POEs) formula and structural character of manipulator. Meanwhile, the closed-form solution for each driving joint variables was derived by employing the proposed method with Paden-Kahan sub-problem method. A mapping relationship between the plücker coordinates of the object and the location information of end-effector was derived through an algebraic method according to the principle of minimum displacement and its operating mode in which the gripper of end-effector should reach the position of the trunk with two labels detected by the robot vision system and be perpendicular to the orientation of the trunk. In addition, the problem of multiple solutions in the inverse kinematics analysis for the harvesting manipulator was solved according to the range of joint variables. Finally, the real-world experiment was performed under laboratory environment. In order to vertify the correctness and obtain the accuracy of the method proposed in this paper. A wooden stick with two markers was placed in the kinematics test platform as the object, which consisted of a laser tracker and a harvesting manipulator. Then, the values of each joint variable could be calculated via the proposed method according to the plücker coordinate data of the markers measured in the object. The results showed that the forest-fruit harvesting manipulator was driven by the solution of inverse kinematics to the position on the stick that its end-effect reached and normal to the stick, which meant this method could meet the requirements of the operating mode. Then ten sets of joint variable values were randomly generated where the positions were measured and the manipulator was sequentially driven by that. The joint variable values were calculated according to the positions through the method proposed in this paper. At last, the calculated results were re-inputted into the controller to drive the manipulator to the new positions. The two measure results on different positions driven by joint variable values generated and calculated were used to obtain the error. The results showed that the maximum position error of end-effector was 6.597 mm, far less than the open size of its gripper, 200 mm, and no more than 3.30%, with the maximum orientation error of 0.975°. The method in this paper was not limited by the specific structure, therefore it is versatile.