Overcoming Redundancy in Solution of the Inverse Kinematics Problem for a Vehicle Operator's Hand

An operator's hand is a spatial mechanism, the configuration of which defines situation and orientation of a robot's hand in space. The biomechanical model of a hand represents a kinematic chain consisting of 18 links with 18 hinges. This design realizes 27 degrees of freedom for the links. Modeling the movements of an operator's hand to a target point is similar to the solution of the feedback problem of positioning in robotics. For complex kinematic structures with a big number of degrees of mobility a solution to this problem involves certain difficulties. At the same time, one of the main problems is the problem of an elbow joint position definition during setting of the final configuration of a person's hand in a target position. This problem can be reduced to the optimization problem with application of a criterion based on the principle of the "lower elbow" described by E. Nakano. Further application of this solution is quite difficult, if it is necessary to model the movement of the higher limb of the operator as a whole, including fingers. Therefore, we have to look for a method, which would allow us to expand the solution, if necessary. At the same time, the method should be simple, reliable and requiring little time and computational complexity. The analysis of the known solutions of the feedback problem of kinematics demonstrated a definite advantage of application of the Forward and Backward Reaching Inverse Kinematics (FABRIK) method. This method excludes the bulkiness and complexity connected with the use of matrices of rotation by direct definition of the situation on a straight line. After definition of new positions of the kinematic chain nodes it is possible without resorting to considerable efforts to calculate the vector of the generalized coordinates. Research of the accuracy of guiding of the operator's hand to the set target position was made in a SimMechanics package of MatLab for checking of the operability of the proposed method. As basic it chose several positions located in the operational space. Movement control of a hand was exercised by the controller, basing his work on FAB-RIK method. During research the following facts were revealed: the maximum error in position of a hand was 1,55 mm; the maximum size of discrepancy to the set orientation was 0,17. Accuracy of the received results confirmed the set re#uirements and the undoubted advantages of the considered method (little computing and time expenditure, simplicity of realization, visually natural pose received due to the solution and also a possibility of work with several final nodes) make it most expedient for application as the solution to the feedback problem of kinematics.

оператор, биомеханическая модель, обратная задача кинематики, кинематическая избыточность, метод прямого и обратного следования, вектор обобщенных координат, целевая позиция, operator, biomechanical model, feedback problem of kinematics, kinematic redundancy, method of direct and return following, vector of the generalized coordinates, target position

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