SPLIT: Sparse Incremental Learning of Error Dynamics for Control-Oriented Modeling in Autonomous Vehicles

TL;DR

The paper addresses the challenge of online, control-oriented vehicle modeling by combining a nominal physical model with a Gaussian Process residual. It introduces SPLIT, which reduces the GP residual input from five dimensions to three via a decomposition into invariant and variable elements, and enforces online learning within a explicitly defined valid region partitioned into subregions. Residual evaluations are sparsified with a Bayesian Committee Machine, enabling real-time, parallel GP inference on streaming data. Across aggressive simulations and real-world experiments, SPLIT achieves faster adaptation, improved control performance, and robust generalization to unseen scenarios, with update times below 0.2 ms and modest memory use, demonstrating the practicality of GP-based residuals in autonomous vehicle control.

Abstract

Accurate, computationally efficient, and adaptive vehicle models are essential for autonomous vehicle control. Hybrid models that combine a nominal model with a Gaussian Process (GP)-based residual model have emerged as a promising approach. However, the GP-based residual model suffers from the curse of dimensionality, high evaluation complexity, and the inefficiency of online learning, which impede the deployment in real-time vehicle controllers. To address these challenges, we propose SPLIT, a sparse incremental learning framework for control-oriented vehicle dynamics modeling. SPLIT integrates three key innovations: (i) Model Decomposition. We decompose the vehicle model into invariant elements calibrated by experiments, and variant elements compensated by the residual model to reduce feature dimensionality. (ii) Local Incremental Learning. We define the valid region in the feature space and partition it into subregions, enabling efficient online learning from streaming data. (iii) GP Sparsification. We use bayesian committee machine to ensure scalable online evaluation. Integrated into model-based controllers, SPLIT is evaluated in aggressive simulations and real-vehicle experiments. Results demonstrate that SPLIT improves model accuracy and control performance online. Moreover, it enables rapid adaptation to vehicle dynamics deviations and exhibits robust generalization to previously unseen scenarios.

Figures (21)

• Figure 1: Challenges of the hybrid modeling paradigm integrating a physical model and a GP-based residual model. (a) Curse of dimensionality. Red circles denote data, while blue lines delineate unit volumes in different feature space dimensions. Accurate GP predictions require sufficient coverage of the feature space, yet the amount of data needed grows exponentially with dimensionality, making dense coverage of high-dimensional vehicle dynamics feature space practically intractable. (b) High evaluation complexity. GP evaluation necessitates computational complexity of $\mathcal{O}(N^3)$. Real-time constraints in controllers limit the feasible training set size, which narrows the applicable operating range of the model and compromises model accuracy. (c) Inefficiency of online learning. Red and blue circles represent new and existing data, while light ellipses denote the marginal gain of each data for feature space coverage. Online learning of GPs requires evaluating the marginal gain of new data and re-evaluating that of existing data, which slows down the learning process and hinders timely adaptation to model deviations.
• Figure 2: Architectural of the vehicle model. The vehicle model consists of a nominal model and a residual model. The parameters $m$, $I_z$, $l_f$, $l_r$, and $C_d$ in nominal model are defined as invariable elements, as their variations are negligible and can be determined through calibration. Conversely, the tire forces $F_{f,x}$, $F_{f,y}$, $F_{r,x}$, and $F_{r,y}$ are defined as variable elements due to their potential fluctuations caused by factors such as temperature, tire pressure, and road surface conditions, which are compensated by the residual model.
• Figure 3: The schematic of the single-track dynamics model. The velocities in vehicle states are depicted in blue, while the tire forces are represented in red.
• Figure 4: Framework of sparse incremental learning. At each sampling cycle, the streaming data are used to update the data subsets within the corresponding subregion in the valid region. The GP predictions from all subsets are aggregated via BCM to estimate the model errors. The estimation is then incorporated into the vehicle model and used by the model-based controller to compute the control inputs, which are subsequently applied to the autonomous vehicle.
• Figure 5: Illustration of the handling curve. The right side shows the effective axle characteristics $F_{f,y}(\alpha_f)/ F_{f,z}$ and $F_{r,y}(\alpha_r)/ F_{r,z}$ of the front and rear axles, while the left side presents the handling curve derived from them. The handling curve is a function of $\alpha_f-\alpha_r$, which increases with the slip angle difference up to a threshold and then ceases to grow.