MMD-OPT : Maximum Mean Discrepancy Based Sample Efficient Collision Risk Minimization for Autonomous Driving
Basant Sharma, Arun Kumar Singh
AI summary
Problem
Current risk-aware planners struggle to accurately minimize collision risk from complex, multi-modal obstacle predictions without excessive sampling or over-conservatism. Existing metrics like CVaR and SAA fail with arbitrary distributions and demand high computational costs for reliable risk estimation.
Approach
The method embeds collision constraint residuals into a Reproducing Kernel Hilbert Space and uses Maximum Mean Discrepancy to approximate risk, combined with a bi-level optimization to select the most informative trajectory samples for efficient planning.
Key results
- Developed a sample-efficient MMD-based collision risk surrogate for arbitrary obstacle distributions
- Introduced a bi-level optimization to select a reduced set of high-value trajectory samples
- Achieved safer planning with fewer samples compared to CVaR and SAA baselines
- Validated real-time performance on synthetic and real-world driving datasets
Why it matters
Enables safer, computationally efficient risk-aware motion planning that can be directly integrated into modern neural trajectory predictors for autonomous vehicles and mobile robots.
Abstract
We propose MMD-OPT: a sample-efficient approach for minimizing the risk of collision under arbitrary pre- diction distribution of the dynamic obstacles. MMD-OPT is based on embedding distribution in Reproducing Kernel Hilbert Space (RKHS) and the associated Maximum Mean Discrepancy (MMD). We show how these two concepts can be used to define a sample efficient surrogate for collision risk estimate. We perform extensive simulations to validate the effectiveness of MMD-OPT on both synthetic and real-world datasets. Importantly, we show that trajectory optimization with our MMD-based collision risk surrogate leads to safer trajectories at low sample regimes than popular alternatives based on Conditional Value at Risk (CVaR). Note to Practitioners—Autonomous Driving software stacks have dedicated modules for predicting trajectories of the obsta- cles(neighboring vehicles). Typically, these predictors provide a set of possible future motions for the obstacles, each of which can have different likelihoods of happening. Thus, a key challenge is to reason about collision risk in a given scene based on predicted trajectories, but without being overly conservative. For example, treating each predicted trajectory as a separate obstacle, without any attention to their likelihood, may not allow any feasible motion to the ego-vehicle. Our work addresses this challenge by proposing a probabilistic approach for modeling and minimizing collision risk. Our core impact lies in improving sample efficiency: that is assessing and minimizing collision risk based on just a handful of predicted trajectories for a given obstacle. Our approach can be easily integrated with any deep neural network based trajectory predictors which have become the de facto standard in autonomous driving industry. Our formulation easily extends to applications like indoor navigation with mobile robots, since human trajectory predictors have structural similarity with those deployed in autonomous driving. A practical limitation of our approach is that it requires additional computing power (in the form of GPU accelerators) to achieve real-time performance.