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This paper intends to present a novel optimal trajectory planning method for obstacle avoidance on highways. Firstly, a mapping from the road Cartesian coordinate system to the road Frenet-based coordinate system is built, and the path lateral offset in the road Frenet-based coordinate system is represented by a function of quintic polynomial respecting the traveled distance along the road centerline. With different terminal conditions regarding its position, heading and curvature of the endpoint, and together with initial conditions of the starting point, the path planner generates a bunch of candidate paths via solving nonlinear equation sets numerically. A path selecting mechanism is further built which considers a normalized weighted sum of the path length, curvature, consistency with the previous path, as well as the road hazard risk.

This paper presents an optimal cooperative path planning method considering driver’s driving intention for shared control to address target path conflicts during the driver-automation interaction by using the convex optimization technique based on the natural cubic spline. The optimal path criteria (e.g. the optimal curvature, the optimal heading angle) are formulated as quadratic forms using the natural cubic spline, and the initial cooperative path profiles of the cooperative path in the Frenet-based coordinate system are induced by considering the driver’s lane-changing intention recognized by the Support Vector Machine (SVM) method. Then, the optimal cooperative path could be obtained by the convex optimization techniques. The noncooperative game theory is adopted to model the driver-automation interaction in this shared control framework, where the Nash equilibrium solution is derived by the model predictive control (MPC) approach.