Estimation of Tire Forces and Torques Via Nonlinear Suspension Models and Optimal Control

Tire–road interaction is one of the main factors that affects vehicle performance; however, it is also a critical and complex aspect of vehicle dynamics, as the contact forces and torques are strongly influenced by both road surface properties and rubber characteristics. In this paper, we present an extended methodology to estimate the full set of tire forces and moments, along with internal suspension reactions, using only strain gauge measurements. A nonlinear suspension model, incorporating asymmetric tension–compression materials, is employed to capture the system's mechanical behavior accurately. The proposed approach is validated against a well-established hybrid symbolic–numeric simulation framework, demonstrating good agreement. To address real-world challenges such as sensor faults or missing data, we formulate an optimal control problem (OCP) that reconstructs tire forces and torques from strain measurements while accounting for vehicle dynamics. A key advantage of our method lies in the use of a symbolic modeling framework that automatically generates all required models for both simulation and control. This ensures consistency, reduces manual modeling effort, optimizes computational efficiency, and enables straightforward application to any suspension configuration and setup.