Error-Centric PID Untrained Neural-Net (EC-PIDUNN) For Nonlinear Robotics Control
Waleed Razzaq
TL;DR
This work tackles nonlinear robotics control where traditional PID struggles by introducing EC-PIDUNN, an error-centric untrained neural-network framework that computes PID gains through a dynamic compute layer and a stabilizing factor $\tau$. By inputting the steady-state error $e_t$ and a parameter vector $\rho_t$, the method shapes the output trajectory without requiring training data, and it incorporates an improved PID to stabilize responses. The architecture is validated on Ackermann vehicle dynamics and a pan-tilt mechanism, where it achieves near-critically damped responses with minimal overshoot and faster settling than classical PID. While offering performance gains, the approach incurs computational costs and shows sensitivity to hyperparameters, with noise/disturbance mitigation identified as a key area for future work.
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 (\(τ\)) 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 \( ρ_t \) 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.