Piecewise affine control for fast unmanned ground vehicles

Benine-Neto, Andre; Grand, Christophe · 2012 · Crossref

DOI: 10.1109/iros.2012.6385675

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Summary

This paper addresses the challenge of maintaining stability in fast unmanned ground vehicles (UGVs) that experience skidding due to nonlinear lateral tire forces at high speeds. The authors propose a Piecewise Affine (PWA) state feedback controller designed to coordinate steering and torque distribution inputs, thereby preventing vehicle instability during demanding maneuvers. The motivation stems from the need for autonomous vehicles to operate safely at high velocities on degraded surfaces, where standard linear controllers fail to account for tire force saturation. The methodology begins by modeling the UGV using a simplified single-track nonlinear model that captures lateral translational and yaw motions. The nonlinear lateral tire forces, described by the Pacejka model, are approximated using PWA functions partitioned into three operating regions based on front tire sideslip angles. To facilitate control synthesis, the operating regions are reformulated as ellipsoidal constraints in the state space, assuming understeering behavior where only front tire nonlinearity is significant. The control strategy employs a PWA state feedback law synthesized via an optimization procedure involving Linear Matrix Inequalities (LMIs). This synthesis ensures asymptotic stability by constructing a Piecewise Quadratic Lyapunov (PWQL) function. The authors utilize a V-K iterative method to solve the resulting Bilinear Matrix Inequalities. Additionally, the control effort is distributed between steering angle and differential yaw moment using Gaussian-based weighting parameters that prioritize steering in linear regions and differential torque as tire forces approach saturation. The results are validated through simulations using a nonlinear UGV model with degraded tire-ground adhesion. The study demonstrates that the proposed PWA controller significantly outperforms a conventional linear controller in maintaining path following and stability under these challenging conditions. The simulations confirm that the PWA approach effectively handles the nonlinear behavior of lateral tire forces, reducing skidding and ensuring the vehicle remains stable even when operating near the limits of tire adhesion. The significance of this work lies in its application of PWA control theory to enhance the safety and performance of high-speed autonomous ground vehicles. By explicitly accounting for tire force nonlinearities and utilizing a robust stability framework based on PWQL functions, the proposed controller provides a more reliable solution for autonomous navigation on rough or low-adhesion surfaces. This approach offers a practical extension of linear control methods, enabling safer operation for applications such as search and rescue, surveillance, and transportation where vehicle dynamics are critical.

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• steering pattern