A Multi-Level Simultaneous Minimization Scheme Applied to Jerk-Bounded Redundant Robot Manipulators

In this paper, a multi-level simultaneous minimization (MLSM) scheme is proposed and investigated to remedy the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. The proposed scheme is novelly designed within multiple levels and finally resolved at the jerk level for a jerk-bounded robot motion, which is desirable for engineering applications. More importantly, the correctness of the proposed MLSM scheme is guaranteed by the corresponding theorems. Then, the MLSM scheme is formulated as a dynamical quadratic program (DQP) that is solved by a piecewise linear projection equation neural network (PLPENN). Furthermore, the path-tracking simulations based on a 6-degrees-of-freedom (DOF) robot manipulator substantiate the effectiveness and advantage of the MLSM scheme. Comparisons between the MLSM scheme and the minimum jerk norm (MJN) scheme illustrate that the proposed scheme is superior and more applicable. Finally, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is provided for reproducible engineering applications by researchers and practitioners. Note to Practitioners —This paper is motivated by the inverse kinematics problem of jerk-bounded redundant robot manipulators in practical applications. Note that the joint-angle drift (JAD) and non-zero final joint-velocity (NZFJV) phenomena as well as the occurrence of high joint variables always encountered in the traditional norm-based scheme for robot manipulators, which is not suitable for the real-time control of robots. Besides, it would be appealing and desirable to resolve the robot redundancy at the jerk level for industrial robots in engineering. Therefore, an effective, flexible, and stable solution for such robot manipulators is significant for practitioners. This paper proposes a multi-level simultaneous minimization (MLSM) scheme for practitioners interested in robot kinematics to remedy the JAD and NZFJV phenomena as well as to prevent the occurrence of high joint variables of redundant robot manipulators. Unlike traditional single-level schemes, such as the minimum jerk norm (MJN) scheme, the proposed scheme is designed within multiple levels with distinct physical nature and finally resolved at the jerk level to achieve a desirable performance for the jerk-bounded redundant robot manipulators. Besides, for better understanding of practitioners, the corresponding block diagram and principle interpretation of the MLSM scheme are presented. Simulation studies and comparisons are designed and conducted on a 6-degrees-of-freedom (DOF) robot manipulator to substantiate the effectiveness and superiority of the proposed scheme. Extensive tests with different weighting factors fully verify the flexibility and stable performance of the proposed MLSM scheme. For reproducible engineering applications by researchers and practitioners, the additional validation on the KUKA robot in the virtual robot experimentation platform (V-REP) is further presented.