Abstract

Autonomous vehicles are becoming increasingly widespread in various real-world applications, ranging from manufacturing and transportation to search and rescue operations. To perform these tasks effectively, it is crucial for the vehicle to be capable of solving trajectory tracking, path following, and obstacle avoidance problems. To improve the accuracy of the performed trajectory, the input constraints acting on the robot’s model should be directly included in the control design. Unfortunately, many of the available control algorithms are unable to do so.

In the last two decades of research, Model Predictive Control solutions have been developed to solve the considered control problems for autonomous wheeled vehicles. Nonlinear MPC schemes exploit accurate state predictions, however, the underlying computational demand might not be affordable in strict real-time contexts or when the robot's computation capabilities are limited.
Conversely, linearized MPC approaches, have the important advantage of drastically reducing computational burdens at the expense of more conservative control performance.

This research proposes a novel control paradigm to solve trajectory tracking, path following and obstacle avoidance problems for input-constrained wheeled mobile vehicles. The proposed solutions are applicable to both differential-drive and car-like robots, and they are the result of the combination of Model Predictive Control strategies and feedback linearization techniques.
First, it is shown that if a feedback linearized model of the robot is exploited for predictions in MPC, then the set of admissible inputs for the linearized model is a nonconvex and state-dependant polyhedron, leading to non-convex and computationally expensive optimization problems with local minima issues. Then, a novel worst-case circular approximation of the state-dependent input constraints set is analytically derived and used to design reference tracking controllers that are, by design, recursively feasible and non-conservative.

The proposed predictive control paradigm has been successfully applied in real time to solve trajectory tracking, obstacle avoidance, and formation control problems for mobile robots and autonomous cars.
The effectiveness and benefits of the proposed control framework are shown with simulations and laboratory experiments involving the Khepera IV differential-drive robots and Quanser Qcar, and its performance contrasted with state-of-the-art alternative control solutions.