An Efficient Risk-aware Branch MPC for Automated Driving that is Robust to Uncertain Vehicle Behaviors

TL;DR

The paper tackles safe motion planning for automated driving under uncertain multi-modal behaviors of other vehicles, focusing on unsignalized intersections. It formulates a risk-aware branch MPC (RAMP) using CVaR in its dual form with an ambiguity set $\mathcal{A}_\alpha(p)$ to handle misestimated branch probabilities, and solves the resulting min-max problem with an augmented Lagrangian iLQR trajectory-tree solver that includes a diminishing regularization in the inner maximization. The approach leverages a backward-forward AL-iLQR pass, a parallelizable Q-function structure for shared and branch dynamics, and a projected gradient ascent update for the probability vector $q$, achieving real-time performance (sub-100 ms on hardware) while emphasizing safety over overly optimistic plans. Numerical results on two unsignalized-intersection scenarios show convergence in most cases, reduced risk of unsafe maneuvers compared to nominal BMPC, and informative velocity profiles that reflect cautious early behavior with recovery later on.

Abstract

One of the critical challenges in automated driving is ensuring safety of automated vehicles despite the unknown behavior of the other vehicles. Although motion prediction modules are able to generate a probability distribution associated with various behavior modes, their probabilistic estimates are often inaccurate, thus leading to a possibly unsafe trajectory. To overcome this challenge, we propose a risk-aware motion planning framework that appropriately accounts for the ambiguity in the estimated probability distribution. We formulate the risk-aware motion planning problem as a min-max optimization problem and develop an efficient iterative method by incorporating a regularization term in the probability update step. Via extensive numerical studies, we validate the convergence of our method and demonstrate its advantages compared to the state-of-the-art approaches.

Figures (4)

• Figure 1: Unsignalized intersection-crossing scenario. The other vehicle (in pink) has two potential behavior modes: "Yield" and "Assert". In this case study, the motion predictor assesses the likelihood of each behavior mode and indicates that the other vehicle is more likely to "Yield". However, the behavior mode "Assert" can result in a potential collision. To avoid unsafe motion, the risk-aware branch MPC planner generates a trajectory tree that considers the different behavior modes by taking into account their associated ambiguity. In this example, it focuses more on the behavior mode "Assert" by appropriately reshaping the probability distribution.
• Figure 2: Test scenarios. The ego vehicle (in blue) intends to turn left. (a) Both surrounding vehicles have two potential behavior modes: "Yield" and "Assert", represented by the red and orange arrows, respectively. (b) The upper vehicle exhibits different behavior modes: "TurnLeft" and "GoStraight".
• Figure 3: Box-plots obtained from 500 Monte Carlo simulations: The total number of iterations to solve our risk-aware branch MPC problem (blue dots) is for some cases larger compared to those required to solve the nominal branch MPC problem (orange) in both test scenarios (TS1) and (TS2). The difference is due to the presence of gradually decaying oscillations in the probability update for the case of risk-aware MPC.
• Figure 4: (a) Closed-loop trajectories of risk-aware motion planning: The actual behavior of the red vehicle is to yield, while the green one keeps a constant velocity. Initially, since the ego vehicle (in blue) is unaware of the true intentions of the surrounding vehicles, it slows down and merges behind the green vehicle to mitigate the risk of the red vehicle not yielding. (b) Velocity profile comparison among risk-aware motion planners for two values of the risk parameter $\alpha=0.1$ and $\alpha=0.8$ and the nominal motion planner.