Moment-based risk-bounded trajectory planning for autonomous vehicles

Abstract

Uncertainty in the behavior of agents on the road is arguably one of the greatest challenges preventing the large scale deployment of fully autonomous vehicles on public roads. This uncertainty is complex and challenging to characterize: empirical data shows multi-modal and non-Gaussian distributions of future positions of human driven vehicles. To drive safely, autonomous driving systems should generate prediction distributions of agent future positions that are representative of the uncertainty and use these distributions to plan trajectories with risk bounds (i.e. certificates on risk). Risk-bounded trajectory planning is a challenging problem, especially given the stringent run-time constraints imposed by autonomous driving. Thus, current approaches that are fast enough for autonomous driving are largely restricted to assuming Gaussian sources of uncertainty with linear constraints and model the ego vehicle as a point mass.

To address these limitations, this thesis aims to develop a risk-bounded trajectory planner that can: 1) use multi-modal non-Gaussian predictions of agent positions, 2) account for ego vehicle and agent geometries, and 3) run in real time. To achieve generality, we dene a prediction representation, AMM-PFT, that represents uncertainty in terms of statistical moments of the prediction distribution. This approach provides generality as statistical moments are universal properties of distributions, and we provide methods for computing them from agent predictions. We then develop methods for bounding risk, given an AMM-PFT, by using statistical moments in deterministic inequalities known as concentration inequalities. These concentration inequalities are then encoded in a fixed risk allocation optimization problem, which we show can plan trajectories with 50 time step horizons in 12.9ms on average.

In some scenarios, these concentration inequalities can be excessively conservative, so we develop non-differentiable methods for risk assessment that are tighter, but cannot be directly encoded in a gradient based optimization routine. Instead, these risk assessment methods are used to inform the outer loop that sets the risk allocation for optimizations; we call this algorithm SRAR and show that it can significantly reduce the average cost of trajectories while remaining safe. We provide controlled experiments demonstrating the advantages and stability of our approach, and we also provide demonstrations of our trajectory planning system in a simulation environment where it can safely drive through a neighborhood with multiple uncertain agents to get to its goal destination. We also consider the problem of using prediction distributions of agent actions, such as accelerating and turning.

To use such predictions, we need to compute AMM-PFTs from these action distributions by propagating the uncertainty in actions into uncertainty in positions using nonlinear dynamics models such as the Dubin's Car. While the particle filter and variants of the Kalman filter can perform this propagation approximately, we develop an algorithm, TreeRing, that can search for closed form systems of equations to perform this propagation exactly for discrete time polynomial systems. We show that the Dubin's car can be transformed into a polynomial system, thus allowing us to apply TreeRing to develop a method for exactly computing AMM-PFTs given distributions of agent acceleration and turning. In numerical experiments, we show that it is more accurate than linearized propagation with the Kalman filter and, with a run-time of less than a microsecond per time step, it is much faster than Monte Carlo methods.

While we only explore this particular application of TreeRing, it has the potential to improve performance in other filtering applications.