Safe Distributed Lane Change Maneuvers for Multiple Autonomous Vehicles Using Buffered Input Cells

This paper introduces the Buffered Input Cell as a reciprocal collision avoidance method for multiple vehicles with high-order linear dynamics, extending recently proposed methods based on the Buffered Voronoi Cell [3] and generalized Voronoi diagrams [1]. We prove that if each vehicle’s control input remains in its Buffered Input Cell at each time step, collisions will be avoided indefinitely. The method is fast, reactive, and only requires that each vehicle measures the relative position of neighboring vehicles. We incorporate this collision avoidance method as one layer of a complete lane change control stack for autonomous cars in a freeway driving scenario. We show in simulations that collisions are avoided with multiple vehicles simultaneously changing lanes on a freeway. We also show in simulations that autonomous cars using the BIC method effectively avoid collisions with an aggressive human-driven car. I. BUFFERED INPUT CELL FOR LINEAR SYSTEMS We describe the Buffered Input Cell (BIC), which is developed based on the previously introduced concepts of generalized Voronoi diagrams [1] and the Buffered Voronoi Cell (BVC) [3]. The BIC extends the collision avoidance properties of the BVC to general linear systems by mapping the constraints in position space into the control input space. A. Collision Avoidance with the Buffered Voronoi Cell Consider N robots whose physical geometries are given by closed convex sets O i . Let d(Oi, Oj) = min ‖pi − pj‖, pi ∈ Oi, pj ∈ Oj be the distance between two cars Oi and Oj , and (pij , p ∗ ji) = arg min ‖pi − pj‖, pi ∈ Oi, pj ∈ Oj are the two closest points on the cars. Then the generalized Voronoi cell [1] of robot i is the set of points q ∈ R that satisfies Vi := {q | ‖q − pij‖ < ‖q − pji‖,∀j 6= i}. Note the strict inequality means that the generalized Voronoi cell is an open set (does not contain its boundary), unlike the standard Voronoi cell, which is closed (does contain its boundary). We use the fact, to be proved later, that a robot is contained in its generalized Voronoi cell if and only if it is in a collision-free configuration. We then define the Buffered Voronoi Cell V̄ i := V i O i , (1) This work was supported in part by the Toyota SAIL Center for AI Research. We are grateful for this support. 1Mingyu Wang is with the Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA, [email protected]. 2Zijian Wang and Mac Schwager are with the Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA, {zjwang, schwager}@stanford.edu. 3 Shreyasha Paudel is with the Ford Research and Innovation Center, Palo Alto, CA 94304, USA, [email protected]. Voronoi cell BVC in position space Vehicle with geometry * BIC in control space +(-)