This paper is focused on planning fast, accurate, and optimal trajectories for autonomous parking. Nominally, this task should be described as an optimal control problem (OCP), wherein the collision-avoidance constraints guarantee travel safety and the kinematic constraints guarantee tracking accuracy. The dimension of the nominal OCP is high because it requires the vehicle to avoid collision with each obstacle at every moment throughout the entire parking process. With a coarse trajectory guiding a homotopic route, the intractably scaled collision-avoidance constraints are replaced by within-corridor constraints, whose scale is small and independent from the environment complexity. Constructing such a corridor sacrifices partial free spaces, which may cause loss of optimality or even feasibility. To address this issue, our proposed method reconstructs the corridor in an iterative framework, where a lightweight OCP with only box constraints is quickly solved in each iteration. The proposed planner, together with several prevalent optimization-based planners are tested under 115 simulation cases w.r.t. the success rate and computational time. Real-world indoor experiments are conducted as well.

This letter is focused on the time-optimal Multi-Vehicle Trajectory Planning (MVTP) problem for multiple car-like robots when they travel in a tiny indoor scenario occupied by static obstacles. Herein, the complexity of the concerned MVTP task includes i) the non-convexity and narrowness of the environment, ii) the nonholonomy and nonlinearity of the vehicle kinematics, iii) the pursuit for a time-optimal solution, and iv) the absence of predefined homotopic routes for the vehicles. The aforementioned factors, when mixed together, are beyond the capability of the prevalent coupled or decoupled MVTP methods. This work proposes an adaptive-scaling constrained optimization (ASCO) approach, aiming to find the optimum of the nominally intractable MVTP problem in a decoupled way. Concretely, an iterative computation framework is built, wherein each intermediate subproblem contains only risky collision avoidance constraints within a certain range, thus being tractable in the scale. During the iteration, the constraint activation scale can change adaptively, thereby enabling to promote the convergence rate, to recover from an intermediate failure, and to get rid of a poor initial guess. ASCO is compared versus the state-of-the-art MVTP methods and is validated in real experiments conducted by a team of three car-like robots.

Optimization-based methods are commonly applied in autonomous driving trajectory planners, which transform the continuous-time trajectory planning problem into a finite nonlinear program with constraints imposed at finite collocation points. However, potential violations between adjacent collocation points can occur. To address this issue thoroughly, we propose a safety-guaranteed collision-avoidance model to mitigate collision risks within optimization-based trajectory planners. This model introduces an “embodied footprint”, an enlarged representation of the vehicle’s nominal footprint. If the embodied footprints do not collide with obstacles at finite collocation points, then the ego vehicle’s nominal footprint is guaranteed to be collision-free at any of the infinite moments between adjacent collocation points. According to our theoretical analysis, we define the geometric size of an embodied footprint as a simple function of vehicle velocity and curvature. Particularly, we propose a trajectory optimizer with the embodied footprints that can theoretically set an appropriate number of collocation points prior to the optimization process. We conduct this research to enhance the foundation of optimization-based planners in robotics. Comparative simulations and field tests validate the completeness, solution speed, and solution quality of our proposal.

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.

This study is focused on the maneuver planning problem for a tractor-trailer vehicle in a curvy and tiny tunnel. Due to the curse of dimensionality, the prevalent sampling-and- search-based planners used to handle a rigid-body vehicle well become less efficient when the trailer number grows or when the tunnel narrows. This fact also has impacts on an optimization-based planner if it counts on a sampling-and-search-based initial guess to warm-start. We propose an optimization-based maneuver planner that weakly relies on the sampling and search, hoping to get rid of the curse of dimensionality and thus find optima rapidly. The proposed planner comprises three stages: stage 1 identifies the homotopy class via A* search in a 2D grid map; stage 2 recovers the kinematic feasibility with softened intermediate problems iteratively solved; stage 3 finds an optimum that strictly satisfies the nominal collision-avoidance constraints. Optimization-based planners are commonly known to run slowly, but this work shows that they have obvious advantages over the prevalent sampling-and-search-based planners when the solution space dimension is high and/or the constraints are harsh.