Inversion-Based Control for Autonomous Racing and Navigation

Abstract

Classical geometric path-following controllers for autonomous ground vehiclescompute steering commands from cross-track and heading error. However, they do not directly check whether the requested motion can be achieved by the vehicle under tire force and friction limits. This thesis develops an iterative force-consistency inversion framework for the complementary problem: given an achievable trajectory demand and a vehicle model that is close enough to the real plant, compute a set of steering and longitudinal inputs that make the nonlinear tire-force model realize that demand. The needed inverse is solved online with a Newton or Levenberg--Marquardt update step using an enhanced bicycle model with nonlinear tire forces, load transfer, roll dynamics and steering lag. The central result is that a pure feedforward inverse alone is not sufficientfor path tracking because model error produces steady-state drift. To compensate for this, the inverse must be paired with an outer error-feedback loop. In simulations, improving the internal model from a kinematic approximation to the enhanced physics model lowers the RMS cross-track error of the feedback inverse on runs that stay within the track. This model improvement also increases the number of runs that leave the track bounds. A model-fidelity sweep across track shapes and speeds shows the limit of the current residual-correction layer: SINDy, Koopman/EDMD, and GP-SSM residual models can be fit using replay data, but they increase closed-loop failures when inserted directly into the Newton inverse. Model fidelity and closed-loop stability must be assessed together; learned residual corrections fit the replay data well but have not yet produced a closed-loop performance gain. Planning under drift and friction constraints provides the trajectory-feasibilityfront end to this inverse-control problem. The planner tests whether a demanded trajectory or acceleration profile lies inside the available friction budget, and whether the path must be reshaped before inversion can produce meaningful inputs. The physical RC-car platform, equipped with dual IMUs, a 360° LiDAR, OptiTrack integration, telemetry, logging, and state estimation, provides the pipeline for future hardware validation. All quantitative controller benchmarks reported in this thesis are simulation-only. The hardware closed-loop controller comparison is reserved for future work.