The study proposes a novel formulation of the inverse kinematics (IK) problem that aims to minimize the joint motion cost while realizing the desired end-effector position and orientation. The constrained optimization problem is converted into an unconstrained form and solved using the simultaneous perturbation stochastic approximation with a norm-limited update vector (NLSPSA) algorithm.
The key highlights and insights are:
The proposed method is simple to implement as it only requires forward kinematics mapping and does not need explicit calculations of the Jacobian or Hessian, unlike traditional gradient-based IK methods.
The NLSPSA-based algorithm exhibits high computational efficiency, requiring only two function evaluations per iteration regardless of the manipulator's degrees of freedom. This makes the proposed approach well-suited for highly redundant manipulators.
The algorithm is numerically stable, even in singular configurations, due to the stochastic nature of NLSPSA and the norm-limited update mechanism.
By explicitly considering the joint motion cost in the optimization problem, the proposed method provides practical IK solutions that yield efficient and compact robot movements, avoiding impractical postures with excessive joint motions.
The flexibility and versatility of the proposed approach are demonstrated through its application to 8-DOF and 20-DOF redundant manipulators with minimal modifications, unlike traditional methods that require specific derivations or training for each manipulator.
The proposed IK computation strategy bridges the gap between gradient-based and metaheuristics-based methods, inheriting the advantages of both approaches. It has the potential to enhance the flexibility and safety of manufacturing systems by enabling efficient and autonomous robot operations, thereby promoting the realization of Industry 4.0.
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