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Optimal path planning of multi-robot in dynamic environment using hybridization of meta-heuristic algorithm

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Abstract

This paper investigates an innovative strategy for generating a collision and deadlock-free optimal position for the individual robots by satisfying the constraints of a dynamic environment for path planning of multiple mobile robots. The current study emphasized the shortfalls of the previous investigation on multi-robot path planning and offered an energetic methodology through the hybridization of modified Q-learning with the improved version of particle swarm optimization (IPSO) and arithmetic optimization algorithm (AOA). In the current scenario, classical Q-learning is modified through a reward policy and generates the best solution for PSO. The basic PSO is upgraded through the perception of ascendency in human civilization and generates an optimal location in the succeeding iteration using an arithmetic optimization algorithm. The proposed hybrid algorithm primarily highlights evaluating the optimal deadlock and starvation free subsequent positions of every robot from their current position, optimizing the path distance for every robot. The authentication of the projected hybrid procedure has been confirmed through benchmark function, computer real robot through webbots simulator, and simulation. Further, the efficacy of the projected procedure has been confirmed by equating the result achieved from MQL–IPSO–AOA with Q-learning, AOA, and IPSO, and also equating the result of the projected procedure with state-of- arts.

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Abbreviations

S:

Set of states

A:

Set of actions

\(a_{t}\) :

Action at instant t

\(s_{t}\) :

State at instant t

\(s_{t + 1}\) :

Next state

\(r\) :

Radius of the robot

\(\upgamma\) :

Learning factor

\(\alpha_{i}\) :

Learning rate

\(Q_{t}^{i}\) :

Q value for \(i{\text{th}}\) agent at instant t

\(s_{t}^{i}\) :

State of agent i at instant t

\(a_{t}^{i}\) :

Action of agent i at instant t

\(\Delta Q_{t}^{i}\) :

Change of Q value for \(i{\text{th}}\) agent at instant t

\(px_{i}^{goal}\) :

X-coordinate value of goal position for \(i{\text{th}}\) robot

\(py_{i}^{goal}\) :

Y-coordinate value of goal position for \(i{\text{th}}\) robot

\(px_{i}^{curr}\) :

X-coordinate value of current position for \(i{\text{th}}\) robot

\(py_{i}^{curr}\) :

Y-coordinate value of current position for \(i{\text{th}}\) robot

\(px_{ob}\) :

X-coordinate value of obstacle position

\(py_{ob}\) :

Y-coordinate value of obstacle position

Re :

Reward function

M :

Number of actions

N :

Number of states

\(re_{t}^{i}\) :

Reward recognized by the robot \(i\) at time t

\(\left( {re^{goal} } \right)_{t}^{i}\) :

Reward received, when \(i{\text{th}}\) robot reached at destination at time t

\(re_{arrv}\) :

Is a constant

\(G_{i}\) :

Goal position of \(i{\text{th}}\) robot

\(\,P_{i}^{t}\) :

Current position of \(i{\text{th}}\) robot

\(\left( {re^{collision} } \right)_{t}^{i}\) :

Penalty

\(P_{j}^{t}\) :

Present position of \(j{\text{th}}\) robot

\(B_{k}\) :

Position of the current obstacle

\(\left( {re^{rotvel} } \right)_{t}^{i}\) :

Rotational velocities

\(\omega_{g}\) , \(\omega_{\omega }\) , \(\delta\) :

Constant

\(\beta\) :

Angle of each free position

\(vel_{i,d} (t)\) :

Velocity of the \(i{\text{th}}\) particle at t instance for the dth component

\(p_{i,d} (t)\) :

Position of the \(i{\text{th}}\) particle at t instance for the dth component

\(C_{1}\) , \(C_{2}\) :

Learning factors

\(\phi_{1}\),\(\phi_{2}\) :

Random vector

N :

Population size

\(pbest_{i}\) :

Best position of each particle obtained so far for the \(i{\text{th}}\) particle in iteration t

\(gbest_{d} (t)\) :

Best position obtained so far for all particles in t instance

\(f\) :

Fitness function

\(\frac{F}{{F_{\max } }}\) :

Function evaluations ratio

\(lbest\,_{i,d} (t)\) :

Local best position of the particles

M:

Quantity of votes

FV:

Free vector

\(S_{i}\) :

Initial point

\(P_{i - real}\) :

Real path \(i{\text{th}}\) robot

AUTTD:

Average Untraveled trajectory Target Distance

\(TP_{i - real}\) :

Real trajectory path for robot i

\(\phi\) and \(rand_{d}\) :

Randomly generated number

\(f_{i}\) :

Fitness value

\(vo_{Le}\) :

Number of votes assimilated for a particular leader

\(f_{a}\) :

Fitness value of all particles

\(f_{avig}\) :

Average fitness value

\(w_{\max }\) and \(w_{\min }\) :

Maximum and minimum value of \(w\)

\(w\) :

Scalar factor inertia weight

\(w_{{\text{int}}}\) :

Intermediate value of the range \(w\)

\(\lambda_{1}\) and \(\lambda_{2}\) :

Control parameter

MOA:

Mathematical optimizer accelerator function

\(vel_{i}^{curr}\) :

Current Velocity of \(i{\text{th}}\) robot

\(R_{i}\) :

\(i{\text{th}}\) Robot

\(px_{i}^{next}\) :

X-coordinate value of next position for \(i{\text{th}}\) robot

\(py_{i}^{next}\) :

Y-coordinate value of next position for \(i{\text{th}}\) robot

\(R_{j}\) :

\(j{\text{th}}\) Robot

\(r_{i}\) :

Radius of \(i{\text{th}}\) robot

\(r_{j}\) :

Radius of \(j{\text{th}}\) robot

\(r_{r}\) and \(r_{o}\) :

Radius of the robot and radius of the obstacle

\(s(i)\) :

Value of \(i{\text{th}}\) sensor

\(px_{R}\) :

X-coordinate value of the robot

\(py_{R}\) :

Y-coordinate value of the obstacle

\(MOA(t)\) :

Value of the function at \(t\) iteration

\(\max \_V\) and \(\min \_V\) :

Maximum(0.9) and minimum values(0.3) of MOA function

\(P_{i,j} (t + 1)\) :

\(j{\text{th}}\) The position vector of \(i{\text{th}}\) solution in the next iteration

\(P_{gbest,j} (t)\) :

\(j{\text{th}}\) Best position obtained

\(U_{j}\) and \(L_{j}\) :

Upper and lower bound value of the \(j{\text{th}}\) position

\(\eta\) and \(\rho\) :

Control parameter

\(MOP(t)\) :

Mathematical optimizer probability

\(P_{ij}\) :

Collision free path

\(P_{i}^{curr}\) :

Initial position vector for the \(i{\text{th}}\) robot

\(Dis(j,ob)\) :

Distance among obstacles and \(j{\text{th}}\) robot

\(px_{ob}\) :

X-coordinate value of the obstacle

\(\,py_{ob}\) :

Y-coordinate value of the obstacle

\(V_{r}\) :

Velocity of the robot

\(V_{o}\) :

Velocity of the obstacle

\(Vel_{ro}\) :

Relative velocity

\(sd\) :

Safe distance between robot and obstacle

\(\beta_{i}\) :

Angle between next position of the \(i{\text{th}}\) robot and obstacle

D:

Distance between the next position and previous position

\(d\) :

Distance between next position of the robot and obstacle

SR:

Sensor vector

\(Th\) :

Threshold value

\(\theta_{T}\) :

Angle between the obstacle and robot

UTTD:

Uncovered trajectory target distance

\(ATTPD\) :

Average total trajectory path deviation

\(ATTPT\) :

Average total trajectory path traversed

\(TP_{ik}\) :

Trajectory path from \(i{\text{th}}\) position to \(j{\text{th}}\) position

References

  • Anandkumar, R.: Hybrid fuzzy logic and artificial Flora optimization algorithm-based two tier cluster head selection for improving energy efficiency in WSNs. Peer-to-Peer Netw. Appl. 14(4), 2072–2083 (2021)

  • Ahn, H., Park, J., Bang, H., Kim, Y.: Model Predictive Control-Based Multirotor Three-Dimensional Motion Planning with Point Cloud Obstacle,” Journal of Aerospace Information Systems, pp.1–15 (2021)

  • Burman, R., Chakrabarti, S., Das, S.: Democracy-inspired particle swarm optimizer with the concept of peer groups. Soft. Comput. 21(12), 3267–3286 (2017)

    Article  Google Scholar 

  • Chiang, H.T., Malone, N., Lesser, K., Oishi, M., Tapia, L.: Path guided artificial potential fields with stochastic reachable sets for motion planning in highlydynamic environments,” IEEE International Conference on Robotics and Automation (ICRA), Washington, pp. 2347–2354 (2015)

  • Das, P.K., Behera, H.S., Panigrahi, B.K.: A hybridization of an improved particle swarm optimization and gravitational search algorithm for multi-robot path planning. Swarm Evolut. Comput 28, 14–28 (2016a)

    Article  Google Scholar 

  • Das, P.K. H. S. Behera, S. Das, H. K.; Tripathy, B. K.; Panigrahi, and S. K. Pradhan: “A hybrid improved PSO-DV algorithm for multirobot path planning in a clutter environment,” Neurocomputing, vol. 207, pp. 735–753 (2016b)

  • Das, P.K., Jena, P.K.: Multi-robot path planning using improved particle swarm optimization algorithm through novel evolutionary operators. Appl. Soft Comput. 92, 106312 (2020)

    Article  Google Scholar 

  • Dewangan, R.K., Shukla, A., Wilfred Godfrey, W.: Three dimensional path planning using Grey wolf optimizer for UAVs. Appl. Intell. 49(6), 2201–2217 (2019)

  • Duan, H., Huang, L.: Imperialist competitive algorithm optimized artificial neural networks for UCAV global path planning. Neurocomputing 125, 166–171 (2014)

    Article  Google Scholar 

  • Duleba, I., Sasiadek, J.Z.: Nonholonomic motion planning based on newton algorithm with energy optimization. IEEE Trans. Control Syst. Technol. 11(3), 355–363 (2003)

    Article  Google Scholar 

  • Ghita, N., Kloetzer, M.: Trajectory planning for a car-like robot by environment abstraction. Robot. Auton. Syst. 60(4), 609–619 (2012)

    Article  Google Scholar 

  • He, W, Qi, X., Liu, L.: A novel hybrid particle swarm optimization for multi-UAV cooperate path planning. Appl. Intell. pp. 1–15 (2021)

  • Jana, M., Vachhani, L., Sinha, A.: A deep reinforcement learning approach for multi-agent mobile robot patrolling”, Int J Intell Robot Appl (2022).

  • Jarrah, R.A., Shahzad, A., Roth, H.: Path Planning and Motion Coordination forMulti-Robots System Using Probabilistic Neuro-Fuzzy. IFAC-Papers OnLine 48(10), 46–51 (2015)

    Article  Google Scholar 

  • Li, G., Xu, H., Lin, Y.: Application of bat algorithm based time optimal control in multi-robots formation reconfiguration. J. Bionic Eng. 15, 126–138 (2018)

    Article  Google Scholar 

  • Li, B., Li-gang, G., Wen-lun, Y.: "An improved artificial bee colony algorithm based on balance-evolution strategy for unmanned combat aerial vehicle path planning," The Scientific World Journal, (2014)

  • Liu, X., Gong, D.: A comparative study of a-star algorithms for search and rescue in perfect maze. In: International Conference on Electric Information and Control Engineering (ICEICE), IEEE, pp. 24–27 (2011)

  • Liu, C., Han, J., An, K.: Dynamic path planning based on an improved RRT algorithm for RoboCup robot. On Robot 39, 8–15 (2017)

    Google Scholar 

  • Long, P., T. Fan, X. Liao, W. Liu, H. Zhang, and J. Pan, "Towards optimally decentralized multi-robot collision avoidance via deep reinforcement learning," IEEE International Conference on Robotics and Automation (ICRA), pp. 6252–6259 (2018)

  • Mishra, A., Sankha, D.: Mobile robot path planning using a flower pollination algorithm-based approach. In: Nature-Inspired Computation in Navigation and Routing Problems, pp. 127–147. Springer, Singapore (2020)

  • Moll, M., Kavraki, L.E.: Path planning for minimal energy curves of constant length," IEEE International Conference on Robotics and Automation, Proceedings. ICRA '04, Vol.3, pp. 2826–2831 (2004)

  • Mohanty, P.K., Parhi, D.R.: A New Efficient Optimal Path Planner for Mobile Robot Based on Invasive Weed Optimization Algorithm, pp. 50–90. Higher Education Press and Springer-Verlag, Berlin Heidelberg (2014)

    Google Scholar 

  • Mohanty, P.K., Parhi, D.R.: Optimal path planning for a mobile robot using cuckoo search algorithm. J. Exp. Theor. Artif. Intell. 28(1–2), 35–52 (2016)

    Article  Google Scholar 

  • Nazarahari, M., Khanmirza, E., Doostie, S.: Multi-objective multi-robot path planning in continuous environment using an enhanced genetic algorithm. Expert Syst. Appl. 115, 106–120 (2019)

    Article  Google Scholar 

  • Paikray, H.K., Das, P.K., Panda, S.: Optimal Multi-robot Path Planning Using Particle Swarm Optimization Algorithm Improved by Sine and Cosine Algorithms. Arab. J. Sci. Eng. 46(4), 3357–3381 (2021)

  • Paikray, H.K., Das, P.K., Panda, S., Balabantaray, B.K.: Improved shuffled frog Leaping Algorithm for Path Planning of multiple Mobile-Robot," IEEE International Conference on Innovations in Electronics, Signal Processing and Communication (IESC), pp. 132–137 (2019)

  • Pamosoaji, A.K., Piao, M., Hong, K.S.: 2019, “PSO-based minimum-time motion planning for multiple vehicles under acceleration and velocity limitations.” Int. J. Control Autom. Syst. 17(10), 2610–2623 (2019)

    Article  Google Scholar 

  • Pradhan, B., Nandi, A., Hui, N.B., Roy, D.S., Rodrigues, J.J.P.C.: A Novel Hybrid Neural Network-Based Multirobot Path Planning With Motion Coordination. IEEE Trans. Veh. Technol. 69(2), 1319–1327 (2019)

    Article  Google Scholar 

  • Rakshit, P., Konar, A.: Learning automata and Niching-Induced Noisy Optimization for Multi-robot Path-Planning. In Principles in Noisy Optimization, pp. 171–242. Springer, Singapore (2018)

    Google Scholar 

  • Rao, D.C., Kabat, M.R., Das, P.K., Jena, P.K.: Cooperative navigation planning of multiple mobile robots using improved krill herd. Arab. J. Sci. Eng. 43(12), 7869–7891 (2018)

    Article  Google Scholar 

  • Salmanpour, S., Motameni, H.: Optimal path planning for mobile robot using Intelligent Water Drops algorithm. J. Intell. Fuzzy Syst. 27(3), 1519–1531 (2014)

    Article  Google Scholar 

  • Sahu, B., Das, P.K., Kabat, M.R.: Multi-robot co-operation for stick carrying application using hybridization of meta-heuristic algorithm. Mathematics and Computers in Simulation, 195, pp.197–226 (2022)

  • Sharma, S., Shukla, A., Tiwari, R.: Multi robot area exploration using nature inspired algorithm. Biol. Inspired Cognit. Architect. 18, 80–94 (2016)

    Article  Google Scholar 

  • Short, A., Bandyopadhyay, T.: Legged motion planning in complex three-dimensional environments. IEEE Robot Autom. Lett. 3(1), 29–36 (2017)

    Article  Google Scholar 

  • Singh, N.N., A. Chatterjee, Am. Chatterjee, and A. Rakshit, “A two-layered subgoal based mobile robot navigation algorithm with vision system and IR sensors,” Emerg. Res.Artif. Intell. Comput. Intell. Commun. Comput. Inf. Sci., vol. 44, pp. 325–334 (2011)

  • Ster, B.: An integrated learning approach to environment modeling in mobile robot navigation. Neurocomputing 57, 215–238 (2004)

    Article  Google Scholar 

  • Sun, Y., Zhang, C., Liu, C.: Collision-free and dynamically feasible trajectory planning for omnidirectional mobile robots using a novel B-spline based rapidly exploring random tree. Int. J. Adv. Rob. Syst. 18(3), 17298814211016608 (2021)

    Google Scholar 

  • Tian, S., Li, Y., Kang, Y., Xia, J.: Multi-robot path planning in wireless sensor networks based on jump mechanism PSO and safety gap obstacle avoidance. Futur. Gener. Comput. Syst. 118, 37–47 (2021)

    Article  Google Scholar 

  • Yi, L.: Study on an improved PSO algorithm and its application for solving function problem. Int. J. Smart Home 10(3), 51–62 (2016)

    Article  Google Scholar 

  • Zhang, Y., Gong, D., Zhang, J.: Robot path planning in uncertain environment using multi-objective particle swarm optimization. Neurocomputing 103, 172–185 (2013)

    Article  Google Scholar 

  • Zhang, J.H., Zhang, Y., Zhou, Y.: Path planning of mobile robot based on hybrid multi-objective bare bones particle swarm optimization with differential evolution. IEEE Access 6, 44542–44555 (2018)

    Article  Google Scholar 

  • Ziadi, S., Njah, M.: PSO optimized F2 based mobile robot motion planning approaches for fixed and mobile targets. Int. J. Intell Robot. Appl. (2022).

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  1. Department of Computer Application, VSSUT, Burla, Odisha, India

    Hemanta Kumar Paikray & Sucheta Panda

  2. Department of Information Technology, VSSUT, Burla, Odisha, India

    Pradipta Kumar Das

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  1. Hemanta Kumar Paikray
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Paikray, H.K., Das, P.K. & Panda, S. Optimal path planning of multi-robot in dynamic environment using hybridization of meta-heuristic algorithm. Int J Intell Robot Appl 6, 625–667 (2022). https://doi.org/10.1007/s41315-022-00256-w

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