Joint Dispatching and Cooperative Trajectory Planning for Multiple Autonomous Forklifts in a Warehouse: A SearchandLearningBased Approach
Abstract
:1. Introduction
1.1. Related Work
1.1.1. Dispatching Methods for Multiple Forklifts
1.1.2. Cooperative Trajectory Planning Methods for Multiple Forklifts
1.1.3. Joint Dispatching and Planning Methods for Multiple Forklifts
1.2. Motivations
1.3. Contributions
1.4. Organization
2. Problem Statement
2.1. Warehouse Layout
2.2. Kinematics of a Forklift Vehicle
3. ANNCombined ScoreBased Dispatching Approach
Algorithm 1: ANN combined scorebased dispatching algorithm 
$\left[{n}_{current},{P}_{i},{P}_{f},{t}_{i}\right]\leftarrow \mathrm{Dispatch}\left(T,F,fail,{P}_{i},{P}_{f},map\right)$

3.1. Vehicle Selection and Initial Pose of a New Subtask
3.2. Scoring System
3.3. ANN Correction Method
3.4. Final Pose Selection
4. Improved Hybrid A* Search Algorithm
Algorithm 2: Improved hybrid A* search algorithm 
$\hspace{1em}\left[\sigma ,Lis{t}_{open}\right]\leftarrow \mathrm{SearchAStar}\left(T,{N}_{c},{P}_{p},{P}_{f},{t}_{p},Lis{t}_{open},Lis{t}_{closed},map\right)$

4.1. Node Expansion Method
4.2. Velocity Planner
4.3. Collision Detection Strategy
Algorithm 3: Collision detection algorithm 
$\hspace{1em}\gamma \leftarrow \mathrm{DetectCollision}\left(T,{N}_{c},{P}_{p},{t}_{p},Lis{t}_{open},map\right)$

4.4. Trajectory Cost Function
5. Joint Dispatching and Cooperative Trajectory Planning Framework
Algorithm 4: Cooperative operation algorithm 
$\hspace{1em}\left[T,F\right]\leftarrow \mathrm{OperateCooperative}\left(T,F,ite{r}_{search},map\right)$

6. Numerical Experiments
6.1. On the Performance of the Trajectory Planning Technique
6.2. On the Performance of Dispatching Strategies
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Abbreviation  Description 

${T}_{1}$  ${v}_{zero}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{zero}$ 
${T}_{2}$  ${v}_{zero}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{mid}$$\mathrm{or}{v}_{mid}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{zero}$ 
${T}_{3}$  ${v}_{mid}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{mid}$ 
${T}_{4}$  ${v}_{mid}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{high}$$\mathrm{or}{v}_{high}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{mid}$ 
${T}_{5}$  ${v}_{high}$$\to \mathrm{Going}\mathrm{straight}\to {v}_{high}$ 
${T}_{6}$  ${v}_{zero}$$\to \mathrm{Turning}\to {v}_{zero}$ 
${T}_{7}$  ${v}_{zero}$$\to \mathrm{Turning}\to {v}_{mid}$$\mathrm{and}{v}_{mid}$$\to \mathrm{Turning}\to {v}_{zero}$ 
${T}_{8}$  ${v}_{mid}$$\to \mathrm{Turning}\to {v}_{mid}$ 
${T}_{9}$  ${v}_{zero}$$\to \mathrm{Lane}\mathrm{changing}\to {v}_{zero}$ 
${T}_{10}$  ${v}_{zero}$$\to \mathrm{Lane}\mathrm{changing}\to {v}_{mid}$$\mathrm{or}{v}_{mid}$$\to \mathrm{Lane}\mathrm{changing}\to {v}_{zero}$ 
${T}_{11}$  ${v}_{mid}$$\to \mathrm{Lane}\mathrm{changing}\to {v}_{mid}$ 
${T}_{12}$  ${v}_{zero}$$\to \mathrm{Stop}\to {v}_{zero}$ 
Current Maneuver  $\mathit{\mu}=0$  $\mathit{\mu}=1$ 

Stop    ${t}_{zero,c}\leftarrow {t}_{zero,p}+{T}_{12}$ ${t}_{mid,c}\leftarrow {t}_{zero,p}+{T}_{12}$ ${t}_{high,c}\leftarrow {t}_{zero,p}+{T}_{12}$ 
Going straight  $\mathbf{if}{t}_{high,p}={t}_{mid,p}$, then ${t}_{zero,c}\leftarrow {t}_{mid,p}+{T}_{2}$ ${t}_{mid,c}\leftarrow {t}_{mid,p}+{T}_{3}$ ${t}_{high,c}\leftarrow {t}_{mid,p}+{T}_{4}$ else ${t}_{zero,c}\leftarrow {t}_{mid,p}+{T}_{2}$ ${t}_{mid,c}\leftarrow {t}_{high,p}+{T}_{4}$ ${t}_{high,c}\leftarrow {t}_{high,p}+{T}_{5}$  ${t}_{zero,c}\leftarrow {t}_{zero,p}+{T}_{1}$ ${t}_{mid,c}\leftarrow {t}_{zero,p}+{T}_{2}$ ${t}_{high,c}\leftarrow {t}_{zero,p}+{T}_{2}$ 
Turning  ${t}_{zero,c}\leftarrow {t}_{mid,p}+{T}_{7}$ ${t}_{mid,c}\leftarrow {t}_{mid,p}+{T}_{8}$ ${t}_{high,c}\leftarrow {t}_{mid,p}+{T}_{8}$  ${t}_{zero,c}\leftarrow {t}_{zero,p}+{T}_{6}$ ${t}_{mid,c}\leftarrow {t}_{zero,p}+{T}_{7}$ ${t}_{high,c}\leftarrow {t}_{zero,p}+{T}_{7}$ 
Lane changing  ${t}_{zero,c}\leftarrow {t}_{mid,p}+{T}_{10}$ ${t}_{mid,c}\leftarrow {t}_{mid,p}+{T}_{11}$ ${t}_{high,c}\leftarrow {t}_{mid,p}+{T}_{11}$  ${t}_{zero,c}\leftarrow {t}_{zero,p}+{T}_{9}$ ${t}_{mid,c}\leftarrow {t}_{zero,p}+{T}_{10}$ ${t}_{high,c}\leftarrow {t}_{zero,p}+{T}_{10}$ 
Parameter  Description  Setting 

$n$  Forklift front overhang length  0.3 m 
$m$  Forklift rear overhang length  1 m 
$l$  Forklift wheelbase  1.5 m 
$2b$  Forklift width  1 m 
$\left[l{b}_{x},u{b}_{x}\right]$  Horizontal boundaries of map  $\left[18,18\right]$ m 
$\left[l{b}_{x},u{b}_{y}\right]$  Vertical boundaries of map  $\left[12,12\right]$ m 
$reso{l}_{xy}$  Node resolution for search algorithms  2 m 
$ite{r}_{pre}$  Maximum iteration in the time dimension involved A* search  500 
$ite{r}_{dispatch}$  Maximum iteration of redispatching  10 
$ite{r}_{search}$  Maximum iteration in the improved A* search  5000 
$\left\{{C}_{1},{C}_{2},\cdots ,{C}_{11}\right\}$  Calibration parameters  $\left\{6,1.5,80,40,6,0.5,4,2,0.5,0.5,3\right\}$ 
$\left\{{T}_{1},{T}_{2},\cdots ,{T}_{12}\right\}$  Modeled time lengths of maneuvers  $\left\{4,2,1.25,0.75,0.5,8,5,3,12,8,5,1\right\}$ s 
${p}_{turn}$  Penalty for turning maneuver  4 
${p}_{lane}$  Penalty for lane changing maneuver  6 
${p}_{inv}$  Penalty for speed inverse maneuver  6 
$\u2206{t}_{i}$  Time postponed when one trajectory planning is failed  10 s 
$\u2206{t}_{cover}$  $\mathrm{Time}$ in Equation (3)  20 s 
$\u2206{t}_{entry}$  Time length after the virtual vehicle entering the rack passage to evaluate $\u2206{t}_{cover}$  20 s 
$\left\{{t}_{claim},{t}_{unload}\right\}$  Time period for picking goods and unloading goods  $\left\{5,5\right\}$ s 
Strategy Name  Filling  Emptying  

Decision Failure Times  End Time (s)  Decision Failure Times  End Time (s)  
ANN combined strategy  38  2388.25  27  2597.25 
Comprehensive strategy  38  2441.00  21  2658.25 
Greedy strategy  135  2768.75  75  3419.00 
Traffic jam removing strategy  120  2709.00  51  3117.75 
Balance strategy  55  2557.75  35  2660.50 
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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
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Zhang, T.; Li, H.; Fang, Y.; Luo, M.; Cao, K. Joint Dispatching and Cooperative Trajectory Planning for Multiple Autonomous Forklifts in a Warehouse: A SearchandLearningBased Approach. Electronics 2023, 12, 3820. https://doi.org/10.3390/electronics12183820
Zhang T, Li H, Fang Y, Luo M, Cao K. Joint Dispatching and Cooperative Trajectory Planning for Multiple Autonomous Forklifts in a Warehouse: A SearchandLearningBased Approach. Electronics. 2023; 12(18):3820. https://doi.org/10.3390/electronics12183820
Chicago/Turabian StyleZhang, Tantan, Hu Li, Yong Fang, Man Luo, and Kai Cao. 2023. "Joint Dispatching and Cooperative Trajectory Planning for Multiple Autonomous Forklifts in a Warehouse: A SearchandLearningBased Approach" Electronics 12, no. 18: 3820. https://doi.org/10.3390/electronics12183820