Inverse kinematic optimization of 7R humanoid arm with joint limits

To solve the kinematic optimization problem of the 7R humanoid arm, the closed-form solutions to the inverse kinematics based on the arm angle parameter were established. The range of the feasible arm angle corresponding to joint limits was determined using analytical methods. Besides, a new function was defined, which is used to evaluate the joint angles, and the optimal indexes of joint limits avoidance were transformed into virtual torques. Based on this, the self-optimizing method was proposed to solve the kinematic optimization problem of joint limits avoidance. Simulations demonstrate that the proposed method can determine the feasible range of the arm angle accurately and implement the kinematic optimization of the humanoid arm efficiently.