Optimal Control and Structurally-Informed Gradient Optimization of a Custom 4-DOF Rigid-Body Manipulator
🤖 AI Summary
To address the challenges of optimal control and physical feasibility for a custom 4-DOF rigid-body manipulator, this paper proposes a centralized control framework that integrates reduced-order Pontryagin’s Maximum Principle (PMP) with full-dynamics-driven, physics-informed gradient descent, enabling dynamics-consistent trajectory planning and closed-form inverse-dynamics input generation. Structurally, joint velocity initialization leverages structural mechanics reaction-force analysis to ensure physically realizable optimization starting points. Symbolic Euler–Lagrange modeling is combined with explicit embedding of rigid-body dynamic constraints to balance model fidelity and computational efficiency. Compared to conventional approaches, the method preserves the theoretical structure of optimal control while significantly improving computational efficiency and physical fidelity. The resulting framework delivers a highly reliable, deployable, real-time control solution tailored for lightweight custom manipulators.
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Develops a control-centric framework for a 4-DOF manipulator
Couples optimal control with physics-informed gradient optimization
Ensures physically admissible trajectories via structural-mechanics initialization
Innovation
Methods, ideas, or system contributions that make the work stand out.
Couples reduced-order PMP controller with physics-informed gradient descent
Uses structural-mechanics analysis to initialize feasible joint velocities
Generates closed-form inverse-dynamics inputs from symbolic Euler-Lagrange model
🔎 Similar Papers
No similar papers found.
