In this paper, we introduce a novel and efficient hybrid trajectory planning method for autonomous driving in highly constrained environments. The contributions of this paper are fourfold. First, we present a trajectory planning framework that is able to handle geometry constraints, nonholonomic constraints, and dynamics constraints of cars in a humanlike and layered fashion and generate curvature-continuous, kinodynamically feasible, smooth, and collision-free trajectories in real time. Second, we present a derivative-free global path modification algorithm to extract high-order state information in free space for state sampling. Third, we extend the regular state-space sampling method widely used in on-road autonomous driving systems to a multi-phase deterministic state-space sampling method that is able to approximate complex maneuvers. Fourth, we improve collision checking accuracy and efficiency by using a different car footprint approximation strategy and a two-phase collision checking routine. A range of challenging simulation experiments show that the proposed method returns high-quality trajectories in real time and outperforms existing planners, such as hybrid A* and conjugate-gradient descent path smoother in terms of path quality, efficiency, and computation resources used.

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

This paper presents a model predictive control (MPC) scheme for the stabilization of high-speed autonomous ground vehicles (AGVs) considering the effect of road topography. Accounting for the road curvature and bank angle, a single-track dynamic model with roll dynamics is derived. Variable time steps are utilized for vehicle model discretization, enabling collision avoidance in the long-term without compromising the prediction accuracy in the near-term. Accordingly, safe driving constraints including the sideslip envelope, zero-moment-point and lateral safety corridor are developed to handle stability and obstacle avoidance. Taking these constraints into account, an MPC problem is formulated and solved at each step to determine the optimal steering control commands. Moreover, feedback corrections are integrated into the MPC to compensate the unmodeled dynamics and parameter uncertainties. Comparative simulations validate the capability and real-time ability of the proposed control scheme.

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

In this paper, we present a more efficient GJK algorithm to solve the collision detection and distance query problems in 2D. We contribute in two aspects: First, we propose a new barycode-based sub-distance algorithm that does not only provide a simple and unified condition to determine the minimum simplex but also improve the efficiency in distant, touching, and overlap cases in distance query. Second, we provide a highly efficient implementation subroutine for collision detection by optimizing the exit conditions of our GJK distance algorithm, which shows dramatic improvements in run-time for applications that only need binary results. We benchmark our methods along with that of the well-known open-source collision detection libraries, such as Bullet, FCL, OpenGJK, Box2D, and Apollo over a range of random datasets. The results indicate that our methods and implementations outperform the state-of-the-art in both collision detection and distance query.