Abstract
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.
Abstract (translated)
这项工作开发了一个定制的四自由度刚体操作臂的控制中心框架，通过结合简化阶次的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来实现。简化的PMP模型提供了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一个直接从完整刚体动力学构建的成本函数来确定相应的时域范围。结构力学反应分析仅用于初始化可行的关节速度——尤其重要的是方位分量的速度，以确保优化器开始于物理上允许的区域内。随后生成的动力学一致的时间范围和运动学轨迹被提供给符号欧拉-拉格朗日模型，从而产生闭式反向动力学输入。此流程在保持严格的控制理论结构的同时，通过计算高效的方式嵌入操作臂的物理约束与加载行为。
URL
https://arxiv.org/abs/2512.11250
