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<p>The design of point-to-point trajectories for robotic manipulators with flexible joints in closed-loop mode—which necessitates the simultaneous determination of the optimal path and the Maximum Dynamic Load Carrying Capacity (DLCC)—presents a significant challenge. Crucially, existing hybrid approaches often decouple these steps, planning the trajectory first in open-loop before controller design, leading to sub-optimal performance. This paper introduces a novel framework that achieves coherent and simultaneous path design and DLCC determination in a closed-loop context. Our novelty lies in the synergistic integration of the Harmony Search (HS) algorithm for global path profile generation and Differential Game Theory (DGT) for deriving the optimal control strategy (Nash Equilibrium). This co-optimization ensures the path is intrinsically compatible with the controller, enabling full utilization of motor torque capacity. Implementation on the Scout mobile robot demonstrated significant superiority: the combined approach achieved an 27.083% increase in DLCC compared to the open-loop baseline. This validates the efficacy of directly coupling trajectory optimization with closed-loop control synthesis to achieve superior payload capacity and tracking robustness.</p> Graphical Abstract <p></p>

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Closed loop path planning for manipulators: a hybrid approach of meta-heuristic optimization and dynamic game theory

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Habib Esfandiar,
  • Saeed Daneshmand

摘要

The design of point-to-point trajectories for robotic manipulators with flexible joints in closed-loop mode—which necessitates the simultaneous determination of the optimal path and the Maximum Dynamic Load Carrying Capacity (DLCC)—presents a significant challenge. Crucially, existing hybrid approaches often decouple these steps, planning the trajectory first in open-loop before controller design, leading to sub-optimal performance. This paper introduces a novel framework that achieves coherent and simultaneous path design and DLCC determination in a closed-loop context. Our novelty lies in the synergistic integration of the Harmony Search (HS) algorithm for global path profile generation and Differential Game Theory (DGT) for deriving the optimal control strategy (Nash Equilibrium). This co-optimization ensures the path is intrinsically compatible with the controller, enabling full utilization of motor torque capacity. Implementation on the Scout mobile robot demonstrated significant superiority: the combined approach achieved an 27.083% increase in DLCC compared to the open-loop baseline. This validates the efficacy of directly coupling trajectory optimization with closed-loop control synthesis to achieve superior payload capacity and tracking robustness.

Graphical Abstract