Predictive Coupled Control of the Road Train Longitudinal and Lateral Motion on a Curved Path

Abstract

In this paper, we consider the problem of a road train path-following on a curved path with an optimal velocity. To solve the problem, we propose a control algorithm based on the coupled model predictive control strategy. Model predictive control assumes the computation of a control sequence by solving an optimal control problem on a finite horizon for a current state of a nonlinear time-varying system. We use the truck steering angle and road train acceleration as control inputs. We describe the road train longitudinal and lateral dynamics using an implicit nonlinear model in continuous time. To derive a discrete linear time-varying state-space prediction model describing the deviations of system dynamics from a reference path we use the Euler method to discretize the original system and compute analytical formulae for its Jacobian by MATLAB Symbolic Math Toolbox. We calculate the reference path and corresponding reference values of the state vector applying the well-known geometric techniques, which utilize the path coordinates and its curvature information. We take the reference values of a truck and a semitrailer yaw angles to be equal. Thus, the reference value of the jackknifing angle is zero. The calculations of reference velocity take into account its skid and rollover limits. To validate the proposed path-following algorithm on the road train we design a simulation model in Simulink. The paper presents the simulation results of testing the movement of a road train along a given path for various values of the reference speed. We show that the algorithm provides high enough reference path-following accuracy, vehicle reference speed tracking, and low values of the jackknifing angle on the speed values up to 18 m/s and curvature radii down to 250 m. The proposed algorithm can be used in ADAS-systems and autonomous vehicles development.