Wu, Xiaofei2025-09-152025-09-152025-09-152025-09-12https://hdl.handle.net/10012/22423Autonomous Driving (AD) has been studied in the past decade and has been gradually deployed in everyday life. A key factor in increasing people’s level of acceptance is trust, which may be enhanced by personalized autonomous driving. One way to design personalized autonomous vehicles is by mimicking the driver’s own driving style while driving safely. Many existing works explore learning-based approaches to achieve this goal. However, the performance of these methods is highly dependent on sample efficiency, and it is usually difficult to enforce safety guarantees. To mitigate these difficulties, this thesis proposes an autonomous vehicle control framework in the form of a parameterized nonconvex trajectory optimization problem with a bilevel structure, where the upper-level models the driving style of a target driver and the lower-level performs vehicle motion planning. Therefore, the focus of this work is the formulation of this parameterized nonconvex trajectory optimization problem and its solution methods, discussed under an application scenario of personalized autonomous vehicles. The lower-level of the bilevel programming problem solves a trajectory optimization problem. The nonlinear dynamic of the vehicle model leads to challenging nonconvex trajectory optimization problems. Many existing approaches formulate them as multistage programs and rely on derivatives of each stage to obtain a local approximation at each iteration, in which case the quality of approximation when solving the optimization program has significant impact on convergence behavior. In this work, we develop a novel approach for obtaining improved local approximations when solving nonconvex trajectory optimization problems. By performing an input-to-state reformulation of system dynamics, we use trajectory sensitivities, which are derivatives of the entire system trajectory with respect to control inputs, to form local approximations. This novel approximation method, when used to solve optimization problem and to linearize the constraints, results in less approximation error than the traditional approach, while the latter has accumulating numerical errors for multi-stage planning problems. Local convergence guarantees for the proposed method are presented for nonconvex optimization problems with input-affine inequality constraints. The method is applied to generate trajectories for an autonomous vehicle that are not dynamically feasible and is extended to include a scenario with static obstacles that introduces nonconvex constraints. The upper-level of the bilevel programming problem models the driving style of the target driver by minimizing the difference between human driving data and motion planning results. The decision variables are weight factors that characterize the driving style and are used to parameterize the lower-level objective, hence affecting its planning results. We adopt a gradient-based approach to solve this problem. However, differentiability is not guaranteed given the bilevel structure and the nonconvex lower-level solution mapping, so we use subgradient "descent" to generalize gradient descent for non-differentiable functions. The quotation marks suggest the fact that subgradient methods are not necessarily monotone. Therefore, a projected subgradient update algorithm is adopted to solve the upper-level problem. When learning-based approaches may fail in rare or unseen scenarios, our proposed method with an embedded vehicle model will continue to work. In addition, the optimization framework with dynamical and safety constraints ensures driving safety. The lower-level motion planner has been simulated on a variety of reference paths and compared with the traditional sequential quadratic programming with conventional first-order Taylor approximation to outperform in approximation accuracy, allowable trust-region radius, iterations to converge, and total solver time. Furthermore, out method is less prone to failure when handling multiple obstacles with a complex reference. The upper-level problem is also simulated to solve tracking problems and obstacle avoidance problems, demonstrating its ability to mimic the driving style of a target driver.ennonconvex optimizationtrajectory optimizationpredictive control for nonlinear systemsautonomous systemsMaster Thesis