A Distributed Multi-Vehicle Coordination Algorithm for Navigation in Tight Environments

TL;DR

The paper tackles safe, real-time coordination of multiple autonomous vehicles operating in tight environments, where centralized planners are impractical. It introduces a distributed NMPC framework that relies on dual decomposition to reformulate collision-avoidance constraints between polytopic vehicle shapes, enabling pairwise, parallelizable optimizations. The main contributions are the alternating optimization scheme that splits trajectory planning from collision avoidance, a dual-based reformulation with strong duality, and a geometric interpretation of dual variables via KKT conditions. The approach demonstrates substantial computational efficiency and scalability on a multi-vehicle platooning scenario, achieving collision-free, near-tight maneuvers with a clear trade-off between maneuver precision and computation time, and it paves the way for extension to 3D planning and uncertain conditions in real-time applications.

Abstract

This work presents a distributed method for multi-vehicle coordination based on nonlinear model predictive control (NMPC) and dual decomposition. Our approach allows the vehicles to coordinate in tight spaces (e.g., busy highway lanes or parking lots) by using a polytopic description of each vehicle's shape and formulating collision avoidance as a dual optimization problem. Our method accommodates heterogeneous teams of vehicles (i.e., vehicles with different polytopic shapes and dynamic models can be part of the same team). Our method allows the vehicles to share their intentions in a distributed fashion without relying on a central coordinator and efficiently provides collision-free trajectories for the vehicles. In addition, our method decouples the individual-vehicles' trajectory optimization from their collision-avoidance objectives enhancing the scalability of the method and allowing one to exploit parallel hardware architectures. All these features are particularly important for vehicular applications, where the systems operate at high-frequency rates in dynamic environments. To validate our method, we apply it in a vehicular application, that is, the autonomous lane-merging of a team of connected vehicles to form a platoon. We compare our design with the centralized NMPC design to show the computational benefits of the proposed distributed algorithm.

Figures (7)

• Figure 1: Centralized design (a) vs. our distributed design (b) for multi-vehicle coordination.
• Figure 2: Top: Primal (a) minimum distance (b) polytope representation (c) optimal solutions. Bottom: Dual: (d) minimum distance (e) separating hyperplane (f) supporting hyperplanes.
• Figure 3: The generated reference trajectories are shown for the example scenario of Fig. \ref{['fig:snapshot_4vehivle']}. The parameter $\rho = 0.5$ for the cyan and green vehicles.
• Figure 4: Four vehicles merge into a platoon in the center lane. The direction of motion is to the right. (a) Snapshots of the simulation are shown with the separating hyperplanes between the vehicles. (b) The state and input trajectories are shown.
• Figure 5: Top: Distance between each pair of vehicles is shown during the cooperative maneuvers. (Distance-gr is the distance between green and red vehicles. Distance-rb is the distance between red and blue vehicles. Distance-gp is the distance between green and pick vehicles. $d_{\textrm{min}}$ is the minimum allowed distance.) Bottom: The solver computation time is reported for each vehicle along the entire maneuver duration.