Autonomous Parking Using Optimization-Based Collision Avoidance

Optimization-Based Collision Avoidance

“…We believe that this is due to the fact that the paths in parallel parking are generally longer than in reverse parking, since the car first needs to drive to the right before it can back into the parking lot, see also We close this section with the following two remarks: First, we point out that, while the paths generated by the Hybrid A are collision-free and kinodynamically feasible, they are challenging to track with low-level path following controllers because they do not incorporate information on the velocity and do not take into account the rate constraints in both steering and acceleration, allowing the car to take "aggressive" maneuveures. As demonstrated in [52], this leads, in general, to significantly longer maneuvering times. Second, we notice from Table 2 that the computation time of Hybrid A is comparable to those of (signed) distance.…”

Adaptive Trajectory Planning and optimization at Limits of Handling

“…Building on the experiences from the racing application, Gray et al [18] considered motion planning at the handling limits for obstacle avoidance, generating a high-level motion plan from a four-wheel dynamic model and a low-level plan using MPC. Zhang et al [19] re-formulate the collision avoidance constraints in the dual variable space, which results in a smooth (but still, nonconvex) optimization problem. A predictive control approach was also utilized by Funke et al [20] and Brown et al [21] to provide collision-free trajectories while maintaining vehicle stability.…”

On Motion Planning Using Numerical Optimal Control

“…In recent years, it has been increasingly popular to apply algorithms from numerical optimal control to compute optimized trajectories online such as in [54,77,87], or in a receding horizon fashion such as the work presented in [22,31,64,74]. The increased interest is mainly due to the development of efficient and reliable 1.2 Publications and contributions 3 optimization algorithms, increased computational resources and the ability to systematically encode problem constraints such as restrictions on how the system can move and actuator limitations within an optimal control framework [53].…”

“…The advantages of using numerical optimal control are that state and control constraints can easily be incorporated in the problem formulation, and that it is straightforward to change the nonlinear model of the system, the performance measure (i.e objective function), and to define and update problem parameters. These methods have in recent years been increasingly popular for real-time motion planning online due to increased computational resources and the development of robust nonlinear optimization algorithms [86].…”

“…Due to non-convex constraints introduced by obstacles and the nonlinear system model, a proper initialization strategy is crucial to converge to a good local optimum [59]. A straightforward initialization strategy is to use linear interpolation between the initial state and terminal state [70], this can however often lead to convergence issues in cluttered environments, which is shown in both Chapter 3 and [87]. A more sophisticated initialization strategy is to use the solution from a samplingbased path planner, for which the path planner in Figure 2.2 aims at finding an initialization from where the nlp solver can converge to a locally optimal solution.…”