Avoidance Trajectories Using Reachable Sets and Parametric Sensitivity Analysis

Abstract

Abstract. The article suggests a conceptual model-based simulation method with the aim to detect collision of cars in all-day road traffic. The benefit of the method within a driver assistance system would be twofold. Firstly, unavoidable accidents could be detected and appropriate actions like full braking maneuvers could be initiated in due course. Secondly, in case of an avoidable accident the algorithm is able to suggest an evasion trajectory that could be tracked by a future active steering driver assistance system. The algorithm exploits numerical optimal control techniques and reachable set analysis. A parametric sensitivity analysis is employed to investigate the influence of inaccurate sensor measurements.

Computation of avoidance regions for driver assistance systems by using a Hamilton‐Jacobi approach

“…The simulations are obtained by using the OCPID-DAE1 Software 20 and following the approach described in other works. 7,33,34 The resulting capture basin for time T = 2 is plotted in Figure 14 (upper graph), and it is in good correspondence with the set obtained by the HJ approach (Figure 14, lower graph). Notice that we can only expect that both computed capture basins are equal up to some accuracy of the order O(Δx) (with Δx = 1 in this figure).…”

“…For this particular scenario, we validate the results by comparing with a direct optimal control approach for calculating the reachable set. The simulations are obtained by using the OCPID‐DAE1 Software and following the approach described in other works . The resulting capture basin for time T =2 is plotted in Figure (upper graph), and it is in good correspondence with the set obtained by the HJ approach (Figure , lower graph).…”

“…Corollary 1. In particular, considering a trajectory reconstruction with time steps t n = nΔt, if at the initial time t 0 = 0, the vehicle and the obstacles are disjoint (ie, condition (31) holds) and if 0 ≤ Δt < Δt where Δt ∶=d∕v andd andv are as in (32)- (33)…”

Semianalytical minimum‐time solution for the optimal control of a vehicle subject to limited acceleration

“…Moreover, other nondynamic constraints() are considered, such as the geometric continuity of the path,() the restrictions on the maximum curvature,() and the avoidance of obstacles. () There are mainly 2 global views of this problem: the first tries to solve in one shot the generation of the path and the optimal law to travel it; the second splits the problem into 2 separate parts: path generation and optimisation of the dynamics. The first approach is done essentially numerically, considering very complex vehicle models, geometric constraints, and various other characteristics, which approximate the real world in a very satisfactory way.…”

Branch-and-lift algorithm for obstacle avoidance control

“…The lack of generic global optimal control solvers has led researchers to develop tailored methods for solving, or at least approximately solving, collision and obstacle avoidance problems to reasonably accuracies [3], [11], [12], [21], [23]. However, these methods are often based on various simplifications or modeling assumptions, which often neglect the dynamics of the system in order to simplify the problem.…”