Error-Centric PID Untrained Neural-Net (EC-PIDUNN) For Nonlinear Robotics Control

TL;DR

This paper introduces EC-PIDUNN, a novel untrained neural network-based PID control architecture that enhances nonlinear robotics control by improving stability and convergence without extensive training.

Contribution

The paper presents a new untrained neural network integrated with an improved PID controller, incorporating a stabilizing factor and dynamic coefficients for better nonlinear system control.

Findings

Outperforms classical PID in convergence and stability.

Achieves nearly critically damped responses in robotics applications.

Effective in nonlinear unmanned ground vehicle and Pan-Tilt systems.

Abstract

Classical Proportional-Integral-Derivative (PID) control has been widely successful across various industrial systems such as chemical processes, robotics, and power systems. However, as these systems evolved, the increase in the nonlinear dynamics and the complexity of interconnected variables have posed challenges that classical PID cannot effectively handle, often leading to instability, overshooting, or prolonged settling times. Researchers have proposed PIDNN models that combine the function approximation capabilities of neural networks with PID control to tackle these nonlinear challenges. However, these models require extensive, highly refined training data and have significant computational costs, making them less favorable for real-world applications. In this paper, We propose a novel EC-PIDUNN architecture, which integrates an untrained neural network with an improved PID controller, incorporating a stabilizing factor (\(\tau\)) to generate the control signal. Like classical PID, our architecture uses the steady-state error \(e_t\) as input bypassing the need for explicit knowledge of the systems dynamics. By forming an input vector from \(e_t\) within the neural network, we increase the dimensionality of input allowing for richer data representation. Additionally, we introduce a vector of parameters \( \rho_t \) to shape the output trajectory and a \textit{dynamic compute} function to adjust the PID coefficients from predefined values. We validate the effectiveness of EC-PIDUNN on multiple nonlinear robotics applications: (1) nonlinear unmanned ground vehicle systems that represent the Ackermann steering mechanism and kinematics control, (2) Pan-Tilt movement system. In both tests, it outperforms classical PID in convergence and stability achieving a nearly critically damped response.