Since the strength of a trapped person often declines with time in urgent and dangerous circumstances, adopting a robot to rescue as many survivors as possible in limited time is of considerable significance. However, as one key issue in robot navigation, how to plan an optimal rescue path of a robot has not yet been fully solved. This paper studies robot path planning for multisurvivor rescue in limited survival time using a representative heuristic, particle swarm optimization (PSO). First, the robot path planning problem including multiple survivors is formulated as a discrete optimization one with high constraint, where the number of rescued persons is taken as the unique objective function, and the strength of a trapped person is used to constrain the feasibility of a path. Then, a new integer PSO algorithm is presented to solve the mathematical model, and several new operations, such as the update of a particle, the insertion and inversion operators, and the rapidly local search method, are incorporated into the proposed algorithm to improve its effectiveness. Finally, the simulation results demonstrate the capacity of our method in generating optimal paths with high quality.
Due to the influence of natural hazards and terrorism, various disasters frequently occur in our world. Since robots are very useful in dangerous or abominable environments where human could not reach certain targets, robot rescue in disaster remains an interesting and challenging subject for researchers [
Up to now, much work has been done on robot path planning using various approaches, such as the cell decomposition [
This paper studies the problem of robot rescue path planning with timeconstraint. Since a robot needs to rescue as many survivors as possible in limited time, the survival time of a survivor is introduced to reflect the feasibility of a path, and the number of rescued survivors is used to evaluate the quality of the path. Based on this, the above problem is formulated as a constraint optimization problem. To solve this problem, a modified PSO algorithm is presented. PSO was originally proposed by Kennedy and Eberhard [
The main contributions of this paper are as follows. (1) The mathematical model of the problem of robot rescue path planning is formulated, considering that a survivor’s survival time is limited; (2) a modified integer PSO is proposed to solve the above model, and several new operators, such as the update of a particle, the insertion and inversion operators, and the rapidly local search method, are incorporated to enhance the capability of the proposed PSO; (3) a series of simulations are done to verify the effectiveness of the proposed method.
The remainder of this paper is organized as follows. Section
There has been much meaningful work on the problem of rescue path planning. In order to search and rescue survivors in a building after a disaster, Kibler et al. constructed a flooding wireless protocol and a flooding fulfill search method and used an autonomous mobile robot as the development platform to verify the effectiveness of the wireless protocol and the search method [
These studies enrich the method of robot rescue path planning. However, the above work omits the fact that a survivor has limited time to wait for rescue, and there have been very few studies on formulating the mathematical model of the rescue problem. Moreover, various intelligent algorithms have been applied to robot path planning but rarely applied to the rescue problem.
PSO is a populationbased stochastic global optimization technique, originated from the simulation of bird flock and fish school seeking food [
Masehian and Sedighizadeh presented two novel PSObased algorithms for robot path planning and evaluated a path based on two criteria. The experiment results empirically verify the effectiveness of the proposed method. However, this method only works for continuous optimization problem [
These studies enrich the method of robot path planning. However, all these approaches do not consider the strength of a trapped person. So, they are not suitable for solving the problem of robot rescue path planning with constraints.
As one key issue in robot rescue, the problem of rescue path planning with time constraint is investigated and formulated in this section.
In order to describe the problem of rescue path planning, the following assumptions are made.
There is only one robot and its power is enough to complete the whole rescue task.
The position of a trapped person (target) is known in advance and fixed during rescue.
Given that the twodimensional workplace contains many targets, the problem of robot rescue path planning can be stated as conducting the rescue task according to the planned path in order to rescue the most targets in limited time. If the strength of a trapped person is smaller than or equal to a threshold set in advance, it is of no necessity to rescue her/him.
Assume that there are
Robot rescue environment.
It is possible that the robot cannot rescue all targets when it follows the sequence given in Figure
The rescue sequence is denoted as
Generally, the value of
In formula (
Overall, the problem of rescue path planning can be formulated as follows:
In order to solve the problem formulated as formula (
Since the problem is NP hard, various methods can be employed to solve it, especially genetic algorithm (GA) and PSO. Both PSO and GA are random search algorithms and suitable for solving the above problem. Though they both have a similar evolutionary process, PSO has memory but crossover and mutation operators which are owned by GA.
Compared with GA, PSO has a different mechanism in sharing information. In GA, information sharing is done among chromosomes. So the whole population moves toward the optimal areas uniformly. While in PSO, only
Besides, PSO has many advantages, such as simple structure, fast convergence, and few parameters to be set. So PSO is employed to solve the above problem in this study, with the purpose of expanding the application range of PSO.
There exist various wellestablished discrete PSO algorithms [
Since the above problem is discrete, a new integer coding method is first introduced to encode a solution; then, a method of updating a particle that is suitable for the integer coding and an approach to updating
For the decision variable,
Considering the swarm with
Traditional methods of updating a particle focus mainly on a continuous numerical optimization problem. Different from the traditional methods, formula (
Although formulas (
The particle after update is denoted as
Assume that
Taking the particle,
For the problem of robot rescue path planning, the number of optimal solutions may be more than one. Some optimal solutions may have the same number of rescued targets but with different rescue sequences. So they correspond to different rescue paths. In order to retain these optimal solutions, the strategy of updating
In traditional PSO,
For the problem investigated in this paper, there may exist the case that different particles have the same fitness. On this circumstance, all particles with the best fitness are first kept in a set, called the optional set
Compared with the traditional method, the above strategy utilizes different
Like most PSObased algorithms, the convergence of our algorithm has a close relationship with the diversity of the swarm. In order to improve the diversity of the swarm, an exchange operator is proposed. For convenient illustration, the concept of entropy is first defined and then used to calculate the diversity of the swarm.
If the probability of the
The diversity of the swarm in generation
If the diversity of the swarm is smaller than a threshold, each particle is performing the exchange operator to generate a new particle. Taking particle
Figure
Exchange operation.
Based on the above strategies, the PSObased rescue path planning can be described as follows.
Initialize the parameters, including the swarm size,
Calculate the diversity of the swarm. If the diversity is smaller than
Update each particle using the method proposed in Section
Perform the rapid local search operator proposed in [
Update
Select
Judge whether the swarm evolves for
Solis and Wets [
For a Borel subset of
Suppose that
Assume that the objective,
From the lemma, we need only to prove that the modified PSO can meet Hypotheses
(1) The iteration function,
(2) Set
In the modified PSO, the velocity of a particle is convergent. These operations have no influences on the result in limited generations, so for
The modified PSO is convergent to the global best solution with the probability of 1.
Since the insertion and inversion operators perform on the set that is used to supply the global best solution, they have the role of transforming the global best solution, so it is enough to prove that the modified PSO converges to the global best solution with the probability of 1, which is equivalent to formula (
only one swarm evolves in the modified PSO;
the global best solution after the above operations is approximate to the current global best solution.
Based on the above assumptions, the velocity updating formula of particle can be written as follows:
Now, obviously, the modified PSO algorithm can be approximated as the traditional PSO, and the particle’s velocity of the traditional PSO model is convergent, so, the velocities of particles in the algorithm can converge to zero, if the number of generations is enough, i.e.,
In order to verify the validity of the proposed method, simulations are done by using MATLAB software on a PC computer. The configuration of PC is P4 and 2.66 GHz, and the RAM memory is 512 M.
The related parameters of PSO are set as follows:
Results of rescuing ten targets.
1  2  3  4  5  6  7  8  9  10 
 

1  4  7  6  5  10  8  2  1  3  9  7 
2  5  6  7  4  9  3  2  8  1  10  7 
3  6  7  4  9  3  2  8  1  5  10  7 
4  7  6  5  8  3  2  9  1  4  10  7 
5  7  6  5  10  8  3  2  1  4  9  7 
Note:
Two different rescue paths with the same number of rescued targets: (a) the rescue path corresponding to row one in Table
Table
Figure
Comparison between the cases with and without the exchange operator.

Average number of rescue paths  

With EO  7  6.3 
No EO  7  2.6 
Note: EO means the exchange operator,
The diversity of the swarm with and without the exchange operator.
Comparison between the cases with and without the exchange operator.

Average number of rescue paths  

With EO  16  1.2 
Without EO  11  11.9 
Table
Table
Comparison with and without the correction operator.




Case 1  7  9 
Case 2  16  21 
Feasibility of solutions  Feasible  Infeasible 
Rescue path without the correction operator for 10 targets.
Table
Comparison between methods of updating the global best particle.




Case 1  7  6 
Case 2  16  14 
Table
Comparison between with and without the rapid local search.




Case 1  7  5 
Case 2  16  13 
Tables
Comparison between local search methods.




Case 1  7  7 
Case 2  16  16 
Comparison of time consumption between local search methods (unit: s).
Mean time of Case 1  Mean time of Case 2  

Rapid local search  26.9  320.3 
Local search  39.8  429.8 
Comparison between the proposed method and integer PSO.




Case 1  7  6 
Case 2  16  12 
Table
Comparison between GA and the proposed method.




Case 1  7  5 
Case 2  16  12 
From Table
For the problem of robot path planning for multisurvivor rescue in limited survival time after a disaster, a modified PSO is proposed to effectively solve it. When formulating the mathematical model of this problem, not only the number of rescued targets is considered but also the survivors’ strength. In order to efficiently solve the established mathematical model by employing PSO, the formulas of updating a particle’s velocity and position are designed. Also a new mechanism of updating
The proposed method is applied to two cases and compared with existing methods, and the simulation results show that the robot can quickly find better rescue paths by the proposed method.
The survivors’ strength is considered when formulating the mathematical model of the problem, and it can reflect realworld rescue scenarios to some degree. However, some assumptions made in this study are too ideal; for example, the velocity of the robot is constant, the rescue environment remains unchanged before and after the disaster, and no obstacles exist in the rescue environment, to say a few, which would limit the application of the proposed method. So in the following research, it is essential to relax the above assumptions so as to better reflect a practical rescue scenario.
In addition, as a realworld rescue environment is much more complex than that considered in this study, some information and parameters are hard to be obtained, which makes the work done not mature enough to be published. It is another topic that needs to be further studied.
The positions of the 100 targets in case two are listed as follows:(70, 0), (60, 25), (82, 40), (80, 80), (20, 45), (15, 65), (36, 87), (41, 22), (95, 50), (2, 11), (73, 10), (60, 35), (8, 50), (20, 90), (20, 55), (15, 76), (36, 70), (41, 12), (95, 52), (12, 17), (76, 8), (60, 15), (29, 30), (80, 70), (20, 35, (15, 55), (36, 47), (41, 12), (95, 40),(2, 31), (71, 20), (60, 70), (11, 90), (89, 20), (20, 2), (15, 40), (36, 65), (41, 6), (95, 40), (2, 15), (70, 27), (60, 10), (88, 40), (26, 60), (20, 30), (15, 32), (36, 65), (41, 60), (95, 80), (25, 10), (70, 35), (60, 42), (80, 28), (60, 0), (20, 45), (15, 50), (36, 15), (41, 10), (95, 9), (2, 22), (74, 28), (60, 18), (80, 69), (82, 28), (20, 40), (15, 18), (36, 23), (41, 94), (95, 21), (8, 14), (70, 22), (60, 23), (80, 24), (80, 30), (20, 26), (15, 75), (36, 76), (41, 15), (95, 71), (21, 85), (70, 14), (60, 63), (70, 55), (80, 80), (20, 14), (15, 99), (36, 60), (41, 11), (95, 100), (20, 52), (0, 19), (25, 71), (40, 51), (84, 80), (45, 45), (65, 65), (87, 87), (22, 22), (50, 50), and (11, 11).
The authors declare no conflict of interests.
This research is jointly supported by the Fundamental Research Funds for the Central Universities (no. 2013XK09), the Jiangsu Planned Projects for Postdoctoral Research Funds (no. 1301009B), and the China Postdoctoral Science Foundation funded project (no. 2014T70557). Thanks to Dr. Edward C. Mignot, Shandong University, for linguistic advice.