Differential-Flatness-Based Path Planning for Semi-Rigid Formations of Ackermann-Steered Vehicles With Obstacle Avoidance

Abstract

This letter presents a geometric path planner for semi-rigid formations of Ackermann-steered vehicles. Differential flatness separates geometric feasibility from the timing law, while fixed Cartesian offsets allow every follower path to be reconstructed from one leader path. A leader–follower curvature relation, valid wherever the follower path is regular, shows how follower steering depends on leader curvature, its spatial variation, and formation geometry. The relation yields explicit leader-level sufficient conditions and a continuous polynomial certificate for formation-wide steering feasibility. The underlying geometry is realized with an intrinsic curvature-profile transcription and a Cartesian flat-output B-spline transcription, while retaining formation-wide separating-hyperplane obstacle avoidance. Experiments on a five-vehicle alternating-baffle corridor and a three-vehicle U-turn, together with controlled ablations, show near-limit follower steering in the corridor and more accepted intrinsic returns in the U-turn under the tested settings. Sequential timings quantify computation for the accepted runs, and dense post-solve checks report overlaps and clearance.