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Vol.:(0123456789)

The Journal of Supercomputing (2024) 80:18009–18047

https://doi.org/10.1007/s11227-024-06155-0

1 3

Research ofhybrid path planning withimproved A*

andTEB instatic anddynamic environments

LinZhang

· NingAn

· ZongfangMa

Accepted: 17 April 2024 / Published online: 9 May 2024

2024

Abstract

In this study, we introduce a new approach to path planning suitable for both

static and dynamic environments. Our method combines the Obstacle Avoidance

Improved A* (OA-IA*) algorithm with the Time Elastic Band (TEB) technique. The

OA-IA* incorporates four key elements: utilization of robot direction information,

adaptive adjustment of bandwidth, enhancement of evaluation function, and path

smoothing operations. We conducted experiments to validate our approach, includ-

ing simulations and real-world veriﬁcations in various environments. In the simula-

tion experiments, we compared our method with two previous approaches: Improved

Local Particle Swarm Optimization (ILPSO) and Obstacle Avoidance RRT (OA-

RRT) method. Across seven diﬀerent simulated maps, the OA-IA* algorithm

showed an average improvement of 0.19 in Path Optimal Degree (POD) compared

to the ILPSO algorithm, along with an average time savings of 11s. Furthermore,

compared to the OA-RRT algorithm, the OA-IA* algorithm achieved an average

POD increase of 0.36, resulting in an average time savings of 60.37 s. Moreover,

we compared our method with APF-RRT*, APF-RRT, RRT, and RRT* approaches

across 50 simulation maps. On average, our method achieved higher POD values

by 0.54, 0.31, 0.85, and 0.26 compared to APF-RRT*, APF-RRT, RRT, and RRT*

methods, respectively. Additionally, the average running time of our method was

signiﬁcantly reduced by 90s, 64.7s, 38.13s, and 19.4s compared to APF-RRT*,

APF-RRT, RRT, and RRT* methods, respectively. In the experimental veriﬁcation

section, we tested our method in a real oﬃce, laboratory, and workshop environ-

ments. In two real-world environments spanning 9.4m

and 9.2m

, our enhanced

A* method integrated with TEB exhibited an average POD value that at least 0.125

higher compared to that of ILPSO combined with TEB. These results demonstrate

the eﬀectiveness of our hybrid path planning method in complex dynamic environ-

ments, achieving optimal outcomes in terms of path length, smoothness, and speed.

In addition, it also ensures the smoothness of the path and speed, and the smooth-

ness is less than 0.05rad/s

Ning An and Zongfang Ma have contributed equally to this work.

Extended author information available on the last page of the article

18010

L.Zhang et al.

1 3

Keywords Hybrid path planning· Time elastic band· Evaluation function

improvement· Path smoothing

1 Introduction

Path planning is crucial in robotics, aiming to ensure obstacle-free movement and

accessibility for robots while considering factors like distance, time, and work cost.

It can be classiﬁed into global and local path planning. Global path planning focuses

on identifying obstacles and deﬁning feasible paths across the entire environment,

while local planning deals with real-time navigation through immediate surround-

ings. Mobile robots rely on intelligent path planning in complex dynamic envi-

ronments, where achieving real-time optimal local planning is challenging. Thus,

studying local path planning in dynamic and unknown environments has become

essential. To address this, a hybrid strategy that combines global and local planning

has emerged, oﬀering higher accuracy and eﬃciency, making it a promising trend in

autonomous navigation.

Currently, there is no one-size-ﬁts-all method for path planning across all envi-

ronments. Nonetheless, the hybrid path planning approach has demonstrated speed

and adaptability in diverse settings. Numerous researchers have introduced vari-

ous techniques for eﬀective path planning. For example, Sang etal. [1] introduced

the MTAPF method to enhance the heuristic A* algorithm for generating globally

optimal paths. This pioneering approach divides the optimal path into multiple sub-

target points, thereby creating a sequential arrangement. By dynamically switching

between these target points, the method signiﬁcantly diminishes the likelihood of

unmanned surface vehicles (USVs) getting trapped in local minima, facilitating a

smoother transition out of such scenarios. Iswanto et al. [2] utilize a fuzzy deci-

sion tree weighted by the Artiﬁcial Potential Field (APF) method to circumvent

local minima and identify the optimal path. Raja et al. [3] integrate the A* and

APF methods for path planning in rugged terrains, aiming to globally optimize ter-

rain roughness while conducting local planning to evade obstacles. AI-Jarrah etal.

[4] combine the bacterial algorithm and fuzzy rules to detect edges in images and

reduce computation time, and this approach can detect edges more precisely along

with reduce the noise in images. An alternative approach involves the integration of

the RRT algorithm with other methods. Ahmed and Ayaz [5] introduce the P-RRT*

algorithm, which combines RRT* with APF to enhance convergence speed. Wang

etal. [6] enhanced the RRT algorithm through the integration of target bias sam-

pling and a reﬁned parent node selection strategy and introduced a DWA algorithm

augmented with fuzzy control of parameters. This innovative approach addresses

the issues of excessive redundant nodes and diminished eﬃciency within the RRT

algorithm while also tackling the challenges associated with limited environmental

adaptability, as well as the complexities surrounding speed and safety considerations

in the conventional DWA method. Yu [7] delves into path planning for multi-robot

scenarios, proposing the NPQ-RRT* algorithm, and it has better dynamic obstacle

avoidance ability. Farzad [8] presents three versions of hybrid method (Adapted-

RRT

GWO

, Adapted-RRT

I−GWO

, and Adapted-RRT

EX−GWO

) for three-dimensional

18011

1 3

Research ofhybrid path planning withimproved A* andTEB in…

path planning for autonomous robots. These methods use the advantages of sam-

pling and metaheuristic methods while eliminating their shortcomings.

Hybrid algorithms that fuse GA with other techniques have demonstrated

enhanced convergence rates and the attainment of optimal solutions. Reference [9]

introduces two novel hybrid algorithms: one combining PSO with the harmony

search algorithm and another merging PSO with GA. These hybrids excel in con-

ducting both exploratory and exploitative searches, and the path obtained avoids all

obstacles. Zhang et al. [10] employ the PSO-GA hybrid algorithm to address the

time-optimized traveling salesman problem, showcasing its eﬀectiveness in optimi-

zation tasks. Furthermore, the synergy of fuzzy logic and PSO has been leveraged to

advance path planning capabilities [11].

In intricate dynamic environments, standalone global or local path planning

approaches often prove inadequate. Hybrid path planning methodologies combine

the virtues of both strategies, yet they demand substantial computational resources

and memory. Balancing stability, robustness, and intelligence poses a challenge in

practical applications. While simplistic and stable algorithms are favored for practi-

cal deployment, sophisticated intelligent algorithms ﬁnd utility in research endeav-

ors. For instance, a reinforcement learning theory incorporating Deep Q-network

(DQN) [12] is harnessed for learning optimal decisions. The A* algorithm stands

out as an eﬃcient and adaptable global path planning method suitable for static envi-

ronments, boasting high planning accuracy and stability. Despite its inherent limita-

tions, ongoing research eﬀorts focus on enhancements to surmount these challenges.

Lin and Chen [13] have enhanced the algorithm’s eﬃciency by reﬁning the heu-

ristic function of A* and the point selection strategy, culminating in a fusion with

the TEB local path planning method. Nonetheless, the author’s reliance on simplis-

tic scenes for both simulation and real-world veriﬁcation experiments renders the

algorithm’s stability challenging to elucidate. The method outlined in this paper

iteratively enhances the A* algorithm across four key stages while concurrently

addressing the smoothness aspect of actual path planning. Crucially, experimental

validation is conducted within both simulated complex environments and real indus-

trial settings, underscoring the method’s applicability across diverse operational

landscapes.

This paper presents two signiﬁcant contributions: (1) Enhancement of the A*

algorithm: The proposed methodology enhances the conventional A* algorithm by

integrating robot direction information, adaptive bandwidth adjustment, reﬁning the

evaluation function, and incorporating path smoothing operations. These enhance-

ments address issues such as irregular paths, collisions in intricate environments,

and constraints in robot control. (2) Adoption of the TEB algorithm for local path

planning: Instead of utilizing the DWA algorithm, this paper advocates for the TEB

algorithm in local path planning. This choice ensures local optimality while main-

taining speed and safety considerations. Through simulation and veriﬁcation experi-

ments, it is demonstrated that the hybrid path planning algorithm, amalgamating

the improved A* and TEB algorithms, facilitates smooth path planning and optimal

speed, rendering it suitable for both static and dynamic environments.

The remainder of this paper is structured as follows. Section 2 introduces the

hybrid path planning method, including the improved global path planning approach

18012

L.Zhang et al.

1 3

and the TEB local path planning method. Section3 outlines the simulation results

and real-world veriﬁcation experiments carried out in both static and dynamic

environments. Finally, Sect.4 summarizes the paper’s contributions and highlights

research directions within this domain.

2 Method

2.1 Improved global path planning method

This paper introduces a novel method named Obstacle Avoidance Improved A*

(abbreviated as OA-IA*) for global path planning. The primary goal is to rectify

the irregular robot movement resulting from abrupt path corners. Our approach

improves the A* algorithm by integrating the principle of obstacle avoidance [14].

The algorithmic workﬂow is illustrated in Fig.1. The OA-IA* algorithm reﬁnes the

heuristic function to ascertain the robot’s rotational direction and angle at inﬂection

points, improving eﬃciency, real-time responsiveness, and the overall smoothness

of the algorithm.

The pseudo-code of the improved A* algorithm step in Fig.1 is described using

the following steps.

Step1: introduce direct information.

Heuristic function:

h(n)=a

⋅

+ b

⋅

cos𝛽 + c

⋅

sin𝛽.

Step2: adaptive bandwidth adjustment.

Deﬁne adaptive step size:

⎧

⎪

⎨

⎪

⎩

max

⋅

+ r

, N

min

, N

≠

Fig. 1 A* algorithm improvement ﬂow chart

18013

1 3

Research ofhybrid path planning withimproved A* andTEB in…

Step3: evaluation function improvement.

Improved evaluation function:

f (n)=g(n)+e

h(n)

[h(n)+p(n)].

Step4: path smoothing.

Parametric equation:

(t)=

(1 − t)

(−2t

+ 2t + 1)P

2.1.1 Introduction ofrobot direction information

The heuristic function of the original A* algorithm only contains distance informa-

tion, and Euclidean distance function is selected to estimate the distance information

of two nodes, which is depicted in Eq. (1).

, y

)

and

, y

)

represent the coordi-

nates of the starting point and the target point, respectively.

In Reference [15], on the basis of Eq. (1), cosine similarity and directional informa-

tion are integrated into the A* algorithm to align the search directions as closely as

possible with the target direction. The closer the research direction is to the direc-

tion of target point, the closer it is to the ideal path, and the higher the optimization

degree of the path. The calculation of the degree of path optimization is detailed

later. Additionally, the heuristic function is

where a, b, and c are static weight,

is the distance information in the traditional

A* algorithm,

𝛽

is the vector angle, one of the vectors is from the starting point

to the target point, and the other is from the parent node to the current child node.

cos𝛽

is the cosine similarity; the range of variation is [

−

1,1].

sin𝛽

is the direction

information.

Equation (2) deﬁnes a heuristic function that integrates distance information,

cosine similarity, and direction information. Nonetheless, this function encounters

challenges related to inconsistent units. To address this issue, we normalize both

the distance and angle components. This normalization enables us to concentrate

exclusively on the impact of cosine similarity and direction information on the path,

thereby eﬀectively resolving the unit inconsistency concern.

2.1.2 Adaptive bandwidth adjustment

The step size serves as a critical parameter in the algorithm. To improve eﬃciency

and safety, we dynamically modify the step size according to the environmental con-

ditions. In regions with sparse obstacles, we augment the step size, whereas in prox-

imity to obstacles, we reduce it. This adaptive approach signiﬁcantly improves per-

formance. The adjustment of the step size depends on two key factors: the quantity

of obstacles within a deﬁned range and their spatial distribution. These factors play

a pivotal role in determining the optimal step size for the mobile robot. Figure2 pro-

vides a visual representation of the robot’s movement direction and obstacle density.

(1)

√

− x

)

+(y

− y

)

(2)

h(n)=a

⋅

+ b

⋅

cos

𝛽

+ c

⋅

sin𝛽

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