Optimal Control and Structurally-Informed Gradient Optimization of a Custom 4-DOF Rigid-Body Manipulator

TL;DR

This paper introduces a control framework for a 4-DOF rigid-body manipulator that combines a reduced-order PMP controller with gradient descent to optimize control parameters while respecting physical constraints.

Contribution

It presents a novel integration of Pontryagin's Maximum Principle with gradient optimization and structural analysis for efficient, physically consistent control of a custom manipulator.

Findings

Closed-form optimal control law derived from PMP

Gradient descent effectively determines time horizons

Physically feasible trajectories generated efficiently

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.