LLA-MPC on Embedded Hardware: Rapid Adaptive Control with Thousands of Parallel Models

I. INTRODUCTION

• LLA-MPC targets rapid dynamics changes by selecting the best-performing candidate model over a short look-back window for receding-horizon control.Its fixed candidate bank is evaluated through one-step predictions, without learning.Source: §I · p. 1

A. Related Work

• LLA-MPC keeps one receding-horizon optimizer while selecting among thousands of nonlinear physics models by batched prediction error.A related online-selection method instead spans models of different fidelity and computational cost [6].Source: A. Related Work · p. 1
• Unlike prior racing approaches based on learned models, residuals, or robust fixed sets, LLA-MPC identifies physical parameters online without training, warm-up data, or fitting.Adaptation occurs within a look-back window of a change rather than after a data-collection phase.Source: A. Related Work · p. 1

B. Contributions

• The work contributes a generalized open-source implementation and hardware validation showing improved performance over a fixed nominal model across tasks, noise levels, and environmental conditions.The implementation has modular dynamics, integrators, and parallelization backends.Source: B. Contributions · p. 1

II. METHODOLOGY

• LLA-MPC directly evaluates a fixed candidate set against recent data, allowing selection to jump to a distant candidate when the window supports it.Identification is local in time and in the visited state-control region; forward simulation is sufficient.Source: §II · p. 2

A. Look-Back Adaptive System Identification

• The candidate bank varies parameters uniformly across their bounded space, and its model rollouts can be parallelized because model arithmetic is shared.Predictions are calculated for all models from the current state and control.Source: A. Look-Back Adaptive System… · p. 2
• At each step, each candidate’s next-state prediction is compared with the observed state using a quadratic residual norm weighted by the state-sensitivity matrix S.The bank is evaluated at the current state and control.Source: A. Look-Back Adaptive System… · p. 2
• The selected model minimizes accumulated residual error over the last W steps, with a parallel sliding window caching residual norms for recursive cost updates.The window maintains cached errors for all K models.Source: A. Look-Back Adaptive System… · p. 2

B. Look-Ahead Model Predictive Control

• The best-fit model at time t is used for MPC from the current state.Source: B. Look-Ahead Model Predictive Control · p. 2
• Controls are bounded at each horizon step, and their changes are also constrained.Source: B. Look-Ahead Model Predictive Control · p. 2
• The optimization uses horizon H, a planner-provided reference trajectory, and running, control-rate, and terminal costs.The previously applied control u−1 is fixed during optimization.Source: B. Look-Ahead Model Predictive Control · p. 2

III. EXPERIMENTAL VALIDATION: EXTREME DRIVING

• A single-track dynamic bicycle model with tire-road interactions is integrated into LLA-MPC.Source: §III · p. 2
• The validation examines LLA-MPC system identification and control on the F1TENTH platform.Source: §III · p. 2
• The evaluation spans a wide range of extreme driving scenarios.Source: §III · p. 2

1) Single-Track Vehicle Model:

• The state comprises inertial pose, body-frame longitudinal and lateral velocities, yaw rate, and driveline wheel speed.Source: 1) Single-Track Vehicle Model · p. 2
• Motor current and road-wheel steering angle are the model controls.Source: 1) Single-Track Vehicle Model · p. 3
• The discrete dynamics are obtained by integrating the continuous dynamics over control period ∆t.Source: 1) Single-Track Vehicle Model · p. 3
• Identified static parameters include vehicle and driveline inertias, axle distances, and wheel radius; drive torque follows a PMSM-control relation.Source: 1) Single-Track Vehicle Model · p. 3

2) Fiala Brush Tire Model:

• The Fiala Tire Model uses a friction-circle constraint inspired by prior work on on-hardware control,.Source: 2) Fiala Brush Tire Model · p. 3
• Per-axle friction limits are calculated from normal loads, with front and rear axles indexed separately.Source: 2) Fiala Brush Tire Model · p. 3
• The coupled front and rear drive wheels and front-only steering determine the slip angles and slip ratios; the front-wheel longitudinal velocity is measured in its steering-wheel frame.Source: 2) Fiala Brush Tire Model · p. 3
• The model combines lateral and longitudinal slip into a resultant magnitude, then models friction cubically up to full sliding and saturates at the friction limit.Source: 2) Fiala Brush Tire Model · p. 3
• Calculated friction is distributed between lateral and longitudinal directions in proportion to the slip components.Source: 2) Fiala Brush Tire Model · p. 3

• The dynamics are deployed with plastic tires that slip at extremely low wheel speeds.Source: B. Experimental Setup · p. 3
• Two configurations pair 180 Hz motion-capture pose with off-board laptop computation up to 40 Hz, or 40 Hz onboard particle-filter pose with computation on a Jetson Orin Nano.Both use 5,000 models integrated by parallel RK4; the Jetson GPU can roll out at least 15,000 models simultaneously at 40 Hz.Source: B. Experimental Setup · p. 3
• Each tracking task compares LLA-MPC with a nominal model identified from rubber-tire, normal-speed driving; success means completing without catastrophic deviation or stopping.Prediction error is evaluated over the next H timesteps from the identified model’s one-step prediction against the measured trajectory.Source: B. Experimental Setup · p. 3
• The Fiala tire-model parameter space has stated lower and upper bounds, and the LLA-MPC window size is W = 60.The MPC optimization horizon is H = 30, with state and control bound violations penalized by a slack cost.Source: B. Experimental Setup · p. 3

C. Experiment 1: Tracking

• At the same average speed as the nominal trajectory, LLA-MPC tracks for over eight laps without crashing, while the nominal controller crashes during its third lap.Source: C. Experiment 1: Tracking · pp. 3–4, Figure 1 · p. 4
• In the low-friction tracking run, both cornering-stiffness and friction estimates converge, and LLA-MPC achieves substantially lower prediction error than the nominal model.Source: Figure 2 · p. 4, C. Experiment 1: Tracking · p. 4

D. Experiment 2: Changing Surfaces

• Over six laps, LLA-MPC completes tracking across changing surfaces, while the nominal controller completes only one lap before lateral drift and slippage cause a crash.LLA-MPC estimates lower friction on low-friction ground and higher friction on higher-grip foam; its predictions have lower average error over the successful run.Source: Figure 3 · p. 4, D. Experiment 2: Changing Surfaces · p. 4

E. Experiment 3: Onboard Compute

• LLA-MPC completes the high-speed drifting maneuver despite noisy state estimation, high initial tire slip, and an adverse environment, while the nominal model crashes.The nominal model follows a wide arc away from the reference trajectory; LLA-MPC also outperforms it in H-step prediction error over the successful run.Source: E. Experiment 3: Onboard Compute · p. 4, Figure 5 · p. 4, Figure 6 · p. 4

IV. FUTURE WORK

• Future work includes uncertainty-weighted look-back costs, broader hyperparameter evaluation, and combining look-back identification with planning, safety, or learning methods.Source: §IV · p. 4