  This paper proposes a novel framework for addressing the challenge of
autonomous overtaking and obstacle avoidance, which incorporates the overtaking
path planning into Gaussian Process-based model predictive control (GPMPC).
Compared with the conventional control strategies, this approach has two main
advantages. Firstly, combining Gaussian Process (GP) regression with a nominal
model allows for learning from model mismatch and unmodeled dynamics, which
enhances a simple model and delivers significantly better results. Due to the
approximation for propagating uncertainties, we can furthermore satisfy the
constraints and thereby safety of the vehicle is ensured. Secondly, we convert
the geometric relationship between the ego vehicle and other obstacle vehicles
into the constraints. Without relying on a higherlevel path planner, this
approach substantially reduces the computational burden. In addition, we
transform the state constraints under the model predictive control (MPC)
framework into a soft constraint and incorporate it as relaxed barrier function
into the cost function, which makes the optimizer more efficient. Simulation
results reveal the usefulness of the proposed approach.
