Kernel-Based Metrics Learning for Uncertain Opponent Vehicle Trajectory Prediction in Autonomous Racing

• Diverse OV policies challenge existing predictors: physics-based methods struggle with long-term interactions, planning-based methods are computationally intensive, and learning-based methods face data scarcity and policy mismatch.Source: §I · p. 1
• The proposed DKL model uses heterogeneous kernel metrics to align similar driving policies and separate dissimilar ones across latent-policy and predicted-state spaces.The alignment is learned from observed EV–OV interactions in an unsupervised manner.Source: §I · pp. 1–2
• The model predicts probabilistic OV trajectories, whose distributions are integrated into EV MPC as dynamic-obstacle constraints for safe and agile overtaking.One-step predictions are recursively sampled to construct multi-step distributions.Source: §I · p. 2
• Experiments with a 1/10th-scale racecar demonstrate the algorithm’s effectiveness quantitatively and qualitatively against existing algorithms.Source: §I · p. 2

A. Physics and planning-based trajectory predictions

• Physics-based predictors struggle with long-term forecasting when they do not account for EV–OV interactions; planning-based predictors rely on assumed OV objectives and can be computationally demanding.Source: A. Physics and planning-based… · p. 2

B. Learning-based trajectory prediction

• Learning-based prediction can generalize poorly in racing because datasets are limited or imbalanced, OV policies vary, and encountered policies may differ from training data.Distance metrics influence representations, but selecting an optimal similarity metric remains unresolved.Source: B. Learning-based trajectory prediction · p. 2

C. Trajectory prediction with uncertainty

• Gaussian processes quantify prediction uncertainty, but stationary kernels can calibrate poorly for non-stationary processes; DKL maps inputs to latent features, though learning complex kernels remains challenging.Source: C. Trajectory prediction with… · p. 2

A. Vehicle dynamics

• The racing vehicles use a dynamic bicycle model with a six-component state for Cartesian position, heading, longitudinal and lateral velocity, and yaw rate.The model is discretized with fourth-order Runge–Kutta, and vehicle pose is also expressed in track-relative Frenet coordinates.Source: A. Vehicle dynamics · p. 3

B. EV trajectory planning problem for racing

• The EV’s MPCC plans over a finite horizon, maximizes race progress while penalizing centerline deviation and control variation, and incorporates the predicted OV trajectory into dynamic-obstacle constraints.The OV safety ellipse scales with predicted-state variance to represent uncertainty in collision avoidance.Source: B. EV trajectory planning problem for… · p. 3

• GPR models OV trajectory prediction from EV–OV interaction patterns as non-parametric Bayesian regression with a GP mean and covariance function.Its posterior distribution provides a mean and covariance calculated from training data.Source: C. GP and DKL for OV trajectory… · p. 3
• The adopted Matérn kernel is stationary and may not capture complex trajectories from diverse OV policies; DKL instead applies the stationary kernel after a nonlinear input transformation.Source: C. GP and DKL for OV trajectory… · p. 3
• Learning the neural feature transformation in DKL without supervision is challenging because EV–OV interactions produce diverse driving policies.Source: C. GP and DKL for OV trajectory… · p. 3

A. Algorithm overview

• The one-step OV state model uses DKL with kernel metrics to address diverse OV driving policies.Source: A. Algorithm overview · p. 3
• Fig. 2 depicts model training in panel (a) and an EV racing algorithm that plans from the predicted OV trajectory distribution in panel (b).Source: Figure 2 · p. 4
• Repeated one-step predictions are sampled to produce a multi-step predicted OV trajectory distribution.Source: A. Algorithm overview · p. 4

B. One-step OV state prediction using DKL

• The DKL input comprises past EV and OV trajectories as interaction patterns, with state information contextualized by track geometry and look-ahead curvatures.Source: B. One-step OV state prediction using… · p. 4
• The nonlinear mapping Φ encodes interaction history as an OV driving-policy representation, using multi-scale filters to capture local and global patterns while preserving causal sequence relationships.Source: B. One-step OV state prediction using… · p. 4
• GPR models the one-step OV state difference as an unknown stochastic process and returns a probability distribution for each output element.Source: B. One-step OV state prediction using… · p. 4
• The four output elements are assumed independent, and their posterior variances capture epistemic uncertainty from policy diversity and aleatoric uncertainty from measurement noise.Source: B. One-step OV state prediction using… · p. 4

C. Kernel-based metrics learning for DKL

• The alignment objective clusters policies with similar output-space behavior and separates dissimilar policies in latent space.Source: C. Kernel-based metrics learning for DKL · p. 4
• Fig. 3 contrasts unaligned features, which are described as more prone to overfitting, with aligned features that improve robustness and prediction performance.Source: C. Kernel-based metrics learning for DKL · pp. 4–5, Figure 3 · p. 5
• The distance-matching loss aligns pairwise distances between latent driving-policy features and OV state-difference outputs, using Matérn kernels.The batch loss matches the two kernel-based distance relationships.Source: C. Kernel-based metrics learning for DKL · p. 5
• Kernel lengthscales govern alignment sensitivity; the framework adjusts latent- and output-space sensitivity to promote clustering of similar data and dispersion of dissimilar data.Fig. 4 illustrates alignment under differing lengthscale relationships.Source: C. Kernel-based metrics learning for DKL · p. 5, Figure 4 · p. 5
• The composite objective combines negative log marginal likelihood with distance and sensitivity losses, which jointly regularize alignment and kernel sensitivity.The authors describe the two added losses as complementary and do not ablate them individually.Source: C. Kernel-based metrics learning for DKL · p. 5

D. Sampling-based multi-step OV trajectory prediction

• Because analytic multi-step prediction is generally intractable, the method rolls out Q sampled OV states across an N-step horizon using consecutive one-step predictions.The rollout updates interaction inputs with predicted EV and OV states and track information.Source: D. Sampling-based multi-step OV… · p. 5
• At each future time step, the multi-step samples define a predicted trajectory distribution summarized by its mean and covariance.Source: D. Sampling-based multi-step OV… · pp. 5–6
• The predicted outcomes define collision-avoidance constraints for safe and agile EV racing maneuvers.Source: D. Sampling-based multi-step OV… · p. 6

A. Experiment setup

• The EV and OV use Jetson AGX Orin and Jetson Orin NX computers, respectively, with control at 20 Hz and multi-step prediction at 10 Hz.Both vehicles run ROS Noetic, exchange state estimates via ROS topics, and use a customized GTSAM-based estimator.Source: A. Experiment setup · p. 6

B. Diverse driving policies of opponent vehicles

• Aggressive OVs block by minimizing lateral distance to the EV, whereas passive OVs omit blocking weights and collision-avoidance constraints.The baseline MPCC uses a planning horizon of N = 12 and a sample time of Ts = 0.1 s; EV and OV speed constraints are 1.9 m/s and 1.6 m/s, respectively.Source: B. Diverse driving policies of… · p. 6
• The training, validation, and test samples are randomly pooled from aggressive and passive interaction datasets without annotations.The prediction model uses an 11-dimensional latent driving policy, 10-step interaction sequences, and 25 trajectory samples.Source: B. Diverse driving policies of… · p. 6

C. Racing results and discussion

• The comparison includes NMPC (GT), CAV, DNN, GPR, DKL, and KM-DKL, with deterministic CAV and NMPC predictions assigned fixed circular uncertainty boundaries.Twenty races are run per baseline, split evenly between passive and aggressive OV policies.Source: C. Racing results and discussion · pp. 6–7
• KM-DKL surpasses all baselines in lateral prediction accuracy, while NMPC (GT) achieves the lowest longitudinal mean error.The reported racing statistics are for OVs with diverse driving policies.Source: Table I · p. 7, C. Racing results and discussion · p. 7
• KM-DKL facilitates agile, safe overtaking without major collisions and meets the 10 Hz real-time requirement despite requiring more computation than the baselines.The paper reports higher collision rates for DKL and DNN than for KM-DKL.Source: C. Racing results and discussion · p. 7

D. Ablation study for unseen driving policy

• The unseen cooperative policy is created by reversing the aggressive policy’s blocking weight, encouraging the OV to move away from the EV’s anticipated path.The comparison evaluates DKL and KM-DKL under this out-of-training-distribution policy.Source: D. Ablation study for unseen driving… · pp. 7–8
• KM-DKL achieves lower NLL than DKL for races against OVs with unseen driving policies.The evaluation uses NLL at the last prediction step, where lower values indicate more accurate uncertainty calibration to unseen data.Source: Figure 7 · p. 8, D. Ablation study for unseen driving… · p. 8

VI. CONCLUSIONS

• The authors identify online learning from streaming interactions and scaling to full-size vehicles as future work, including perception errors and multi-vehicle interactions.The study reports validation on a 1/10th-scale racecar platform.Source: §VI · p. 8