用最优控制与物理约束结合，高效求解四自由度机械臂的运动规划。
Optimal Control and Structurally-Informed Gradient Optimization of a Custom 4-DOF Rigid-Body Manipulator
- 结合庞特里亚金原理与梯度下降，实现闭环最优控制。
- 通过物理约束优化时间尺度，确保轨迹动态一致性。
- 适合需要高精度动力学建模的机器人控制研究者。
本文为定制的4自由度刚体机械臂构建了一个以控制为核心的框架，将简化版庞特里亚金最大值原理（PMP）控制器与物理信息梯度下降阶段耦合。简化PMP模型提供关节加速度的闭式最优控制律，而梯度下降模块则通过最小化直接基于完整刚体动力学构建的代价函数，确定相应的时域。结构力学反分析仅用于初始化可行的关节速度，特别是方位角分量，确保优化器从物理可接受区域开始。生成的运动学轨迹与动态一致的时间尺度被输入符号式欧拉-拉格朗日模型，得到闭式逆动力学输入。该流程在保持严格控制理论结构的同时，以计算高效方式嵌入机械臂的物理约束与载荷行为。
原文摘要 · Abstract (English)
This work develops a control-centric framework for a custom 4-DOF rigid-body manipulator by coupling a reduced-order Pontryagin's Maximum Principle (PMP) controller with a physics-informed Gradient Descent stage. The reduced PMP model provides a closed-form optimal control law for the joint accelerations, while the Gradient Descent module determines the corresponding time horizons by minimizing a cost functional built directly from the full Rigid-Body Dynamics. Structural-mechanics reaction analysis is used only to initialize feasible joint velocities-most critically the azimuthal component-ensuring that the optimizer begins in a physically admissible region. The resulting kinematic trajectories and dynamically consistent time horizons are then supplied to the symbolic Euler-Lagrange model to yield closed-form inverse-dynamics inputs. This pipeline preserves a strict control-theoretic structure while embedding the physical constraints and loading behavior of the manipulator in a computationally efficient way.
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