Receding-Horizon Lattice-Based Motion Planning with Dynamic Obstacle Avoidance

Abstract

A key requirement of autonomous vehicles is the capability to safely navigate in their environment. However, outside of controlled environments, safe navigation is a very difficult problem. In particular, the real-world often contains both complex 3D structure, and dynamic obstacles such as people or other vehicles. Dynamic obstacles are particularly challenging, as a principled solution requires planning trajectories with regard to both vehicle dynamics, and the motion of the obstacles. Additionally, the real-time requirements imposed by obstacle motion, coupled with real-world computational limitations, make classical optimality and completeness guarantees difficult to satisfy. We present a unified optimizationbased motion planning and control solution, that can navigate in the presence of both static and dynamic obstacles. By combining optimal and receding-horizon control, with temporal multi-resolution lattices, we can precompute optimal motion primitives, and allow real-time planning of physically-feasible trajectories in complex environments with dynamic obstacles. We demonstrate the framework by solving difficult indoor 3D quadcopter navigation scenarios, where it is necessary to plan in time. Including waiting on, and taking detours around, the motions of other people and quadcopters.

A path planning and path‐following control framework for a general 2‐trailer with a car‐like tractor

“…Note that the only difference between the OCPs defined in (7) and (9), respectively, is that the initial and goal state constraints are switched. In other words, (7) defines a path planning problem from z I to z G and (9) defines a path planning problem from z G to z I .…”

“…is an optimal solution to the optimal path planning problem (7) with optimal objective functional value J * , then the distancereversed path (z * (s),ū * p (s)),s ∈ [0,s * G ] given by (57)-(58) withs * G = s * G , is an optimal solution to the reverse optimal path planning problem (9) with optimal objective functional valueJ * = J * .…”

“…Note the similarity of OCP in (12) with the optimal path planning problem (7). Here, the obstacle imposed constraints are neglected and the vehicle is constrained to only move forwards.…”

“…which is identical to the optimal path planning problem in (7). Hence, the OCPs in (7) and (9) are equivalent [14] and the invertible transformation relating the solutions to the two equivalent problems is given by (61) ands G = s G . Hence, if an optimal solution to one of the problems is known, an optimal solution to the other one can immediately be derived using (61) ands G = s G .…”

Improved Optimization of Motion Primitives for Motion Planning in State Lattices

“…As will be shown in this work, for good performance it does not only suffice to optimize the behavior between the boundary conditions, but also the conditions themselves. One approach to select the boundary conditions in the set of BVPs to be solved is by manual specification, which is typically done by an expert of the system [3,15]. The manual procedure can be very time-consuming and if some of the system's parameters are altered, the boundary conditions usually need to be carefully re-selected to not unnecessarily restrict the performance possible to obtain, and to maintain feasibility, during the following optimization of the motion primitives.…”