An Adaptive Localization Based Station Keeping for Autonomous Vehicles

Abstract. The problem of localizing a vehicle autonomously has been addressed many a times but finding a better cost function to work with or less parameters/agents to work with is still an area which needs more attention. For localizing a vehicle in a multi-agent environment we are measuring the range and bearing values of a vehicle with respect to other vehicles/beacons present in the environment. Beacon positions are unknown and we are going to use an adaptive least square algorithm to estimate the these and then using the bearing and range data we want to approach the target asymptotically.

Problem Statement. In our problem, we have N beacons S ≜ {S₁,...,S_N}, N ≥ 2, with unknown positions x_i ∈ Rⁿ for each S_i , to localize our vehicle A with current position at y ∈ Rⁿ, n ∈ {2, 3} and desired position at y^* ∈ Rⁿ. We also have the beacon-target distances d^∗_i ≜ || y^∗ − x_i||, beacon-agent distances d_i(t) ≜ ||y(t) − x_i||; beacon-target bearing angle θ^∗_i, beacon-agent bearing angle θ_i(t), and self-position y are available to A. The task is to define a control law to generate ẏ(t) such that for any given initial position y(0) = y₀, y(t) converges to y^∗ asymptotically.

Results.