混合轨迹规划：自动驾驶在复杂环境中的新方法

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“Hybrid Trajectory Planning for Autonomous Driving in Highly Constrained Environments” 本文是一篇关于自主驾驶汽车运动规划的专业论文，提出了一种新颖且高效的混合轨迹规划方法，旨在解决复杂且受限环境中的自动驾驶问题。作者通过仿真实验验证了该算法在处理几何约束、非霍尔动态约束以及车辆动力学约束方面的有效性和效率。文章的关键贡献在于以下几个方面： 1. **混合轨迹规划框架**：该框架结合了多层采样和优化技术，以层次化的方式处理各种约束。这种设计使得算法能够更加人性化地模拟汽车在复杂环境中的行驶行为。 2. **几何约束处理**：在规划过程中，算法考虑了环境中的静态和动态障碍物，以及道路边界等几何限制，确保了车辆能够在不碰撞的情况下安全行驶。 3. **非霍尔动态约束**：汽车的运动受到其非霍尔动态特性（如不能瞬间改变方向）的限制。该方法考虑了这些物理限制，确保生成的轨迹既符合汽车的实际动态又满足安全要求。 4. **动力学约束**：除了考虑汽车的几何和非霍尔动态，还考虑了车辆的动力学性能，如加速度、减速度和转弯半径等，以保证舒适性和稳定性。 5. **仿真实验验证**：为了证明算法的性能，作者进行了详细的仿真测试，这些实验结果证实了所提出的混合规划方法在复杂环境中的有效性，能够在满足各种约束的同时，实现高效且灵活的运动规划。 6. **支持研究**：这项工作得到了中国国家自然科学基金的支持，项目编号分别为91420203和61703041，表明了该研究在学术领域的认可度。该论文为自动驾驶技术提供了一种新的运动规划策略，尤其适用于城市环境中，其中道路狭窄，交通复杂，对车辆的规划能力有很高的要求。这一研究对于提升自动驾驶汽车在实际环境中的安全性和可靠性具有重要意义，并可能对未来智能交通系统的设计产生深远影响。

Y. Zhang et al.: Hybrid Trajectory Planning for Autonomous Driving in Highly Constrained Environments

the feasible solution space in different layers. Our contribu-

tions are:

• We propose an efﬁcient layered trajectory planning

framework. This framework handles each type of

constraint using distinct methods. We ﬁrst handle the

geometry constraints using a search-based global path

modiﬁcation layer, which identiﬁes the shortest path

through the environment without regard for vehicle

motion constraints. The second layer, a multi-stage state

sampling method, samples in the neighbourhood around

the shortest path to generate a kinematically-feasible

path, which resolves the nonholonomic constraints of

the vehicle. In this way, the framework reduces the

infeasible state space region from the potential sampling

space signiﬁcantly. More precisely, it prevents the

state space sampling method from spending computa-

tion resources on generating high-cost kinematically-

feasible paths to sample the infeasible region that is

limited by constraints, which improves the sampling

efﬁciency. Once the best path is found in the sampling

stage, the dynamical constraints of the vehicle (lateral

accelerations and longitudinal accelerations and decel-

erations) are imposed to deﬁne a speed proﬁle. This

approach differs from the hybrid A* and RRT* fami-

lies of methods, which ﬁrst impose nonholonomic

constraints to generate kinematically-feasible motion

primitives, then incrementally construct a sampling

graph using motion primitives to resolve the geometry

constraint. Their strategy leads to swerving paths due

to the discretized or randomized motion primitives. Our

method results in more human-like solutions, by ﬁnding

the best coarse path through the environment ﬁrst, and

then reﬁning the path to meet kinodynamic constraints.

• We introduce a general global path modiﬁcation

algorithm with a derivative-free smoothing process to

extract high order state information for the state space

sampling. A big difference from the origin space explo-

ration method used in the heuristic search path planning

framework [46] is that we provide a derivative free path

smoothing algorithm based on the curve energy function

and ﬁt a B-spline to get the precise orientation and

curvature information of the path. Chen [46] uses the

resulting circle path to limit the search region for the

hybrid A*, which only leverages the position informa-

tion of the circle path. We instead exploit the position,

orientation and curvature information of the smoothed

circle path, leading to more drivable paths. Gu et al.

also propose global path deformation methods (dynamic

programming method [47], elastic band method [48]).

However, these methods require precise road geometry

information to construct the search graph. Our method

only require traversable region information, which can

be easily extended to free space planning scenarios.

• We extend the regular state space sampling method to a

multi-phase deterministic state space sampling method

to handle navigation problems in complex and crowded

environment. Different from the regular state space

sampling methods [21], [25], [49] that use a single

polynomial function to represent naive maneuvers with

only one swerve, our method divides the path plan-

ning problem with nonholonomic constraints to several

consecutive stages and uses curvature-continuous piece-

wise cubic spirals to represent complex maneuvers

(consecutive s shape paths) subject to nonholonomic

constraints of cars. In this way, our planner is not only

able to get rid of high order polynomials that leads to

heavy computations but also provides a long-term path

with a continuous curvature proﬁle aligned with the

geometry of the modiﬁed global path.

• We developed a more efﬁcient and accurate collision

checking method by using a different footprint approx-

imation strategy and a two-phase collision checking

routine.

This paper is organized as follows. The methodology is

presented in Section II, which includes the following subsec-

tions: the global path modiﬁcation, multiple stage state

sampling, optimization-based speed planning, hierarchical

collision checking. Section III explains the experiments

setup and evaluation of the proposed algorithm in details.

Section IV summarizes the contributions and discusses future

work.

II. METHODOLOGY

The overall structure of the hybrid trajectory planning frame-

work is shown in Fig. 3. We ﬁrst create a traversable

region around the global path and set the intersection of

the traversable region and on-board free-space perception

results as the search space of the global path modiﬁca-

tion layer. This pre-processing step restricts the region of

interest and ﬁlters irrelevant obstacles from the motion

planning problem. Next, the global path modiﬁcation layer

employs a novel space exploration method to identify a

collision-free and smooth path inside the aforementioned

search space. A multiple stage state sampling layer is then

applied to sample along the new reference path and identiﬁes

a collision-free, kinematically-feasible, curvature-continuous

desired path. Finally, an optimization-based time-optimal

speed planning layer is employed to construct a speed proﬁle

along the path, taking into account the dynamic constraints of

the vehicle.

A. GLOBAL PATH MODIFICATION

The goal of the global path modiﬁcation layer is to get a

collision-free global path within the region limited by the

original global path and the traversable region from the

perception module. In realistic on-road driving scenarios,

the original global path provided by a high-level route plan-

ning module will not be optimal, and may not even be feasible

due to the presence of obstacles such as parked cars along the

roads and reconstruction cones which appear temporarily. In a

highly curved lane with tight turning radius without obstacles,

following the center line of the lane results in more control

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