Improved Path Planning by Tightly Combining Lattice-Based Path Planning and Optimal Control

Abstract

This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to optimal path planning problems in unstructured environments. The approach is motivated by showing that a lattice-based planner can be cast and analyzed as a bilevel optimization problem. This insight is used to integrate a latticebased planner and an optimal control-based method in a novel way. The lattice-based planner is applied to the problem in a first step using a discretized search space. In a second step, an optimal control-based method is applied using the latticebased solution as an initial iterate. In contrast to prior work, the system dynamics and objective function used in the first step are chosen to coincide with those used in the second step. As an important consequence, the lattice planner provides a solution which is highly suitable as a warm-start to the optimal control step. This proposed combination makes, in a structured way, benefit of sampling-based methods ability to solve combinatorial parts of the problem and optimal control-based methods ability to obtain locally optimal solutions. Compared to previous work, the proposed approach is shown in simulations to provide significant improvements in terms of computation time, numerical reliability and objective function value.

Optimization-Based Maneuver Planning for a Tractor-Trailer Vehicle in a Curvy Tunnel: A Weak Reliance on Sampling and Search

“…Liu et al [4] searched for collision-free waypoints and then connected Reeds-Shepp primitives between adjacent waypoints to form an initial guess for numerical OCP. Bergman et al [20] divided a searched path into segments and solved several subtle OCPs with the two-point boundary conditions of each segment. Li et al [10] proposed an extended hybrid A* to find a coarse path and then solved a series of OCPs with increasing sizes of obstacles toward their nominal ones.…”

“…The progressively constrained optimal control (PCOC) approach [10] is an optimization-based planner that refines the trajectory obtained by EHA. Tightly combining sampling-and-search and optimal control (CSOC) [20] refers to getting a coarse trajectory via EHA and solving local trajectory planning problems along segmented pieces via numerical OCP. The results are reported in Table II.…”

Path Planning for Autonomous Mobile Robots: A Review

“…Examples of roadmaps include Voronoi graphs [ 25 ] (see Figure 2 e), Visibility graphs [ 26 ] and State-Lattice graphs (see Figure 2 f). The latter consist of making the edges based upon motion primitives, so the resulting path is ensured to be feasible given the robot mobility constraints, especially when using Graph Search algorithms, as in the work of Likhachev and Ferguson [ 27 ], Bergman et al [ 28 ].…”

Autonomous Avoidance Maneuvers for Vehicles using Optimization

“…Optimization could be applied on initial trajectories obtained by other means, e.g., by first applying graph search of some predefined motion primitives and then by optimizing the resulting path [50,51]. Even better performance could be reached if the predefined maneuvers are computed for the same criterion as used in the optimization step [52]. For many dynamic situations, where it is challenging to precompute and store sufficiently many maneuvers, sampling techniques, such as inputspace sampling or state sampling [53], are popular since they allow computation of candidate trajectories online [54].…”