Flocking control problem of mobile robots under environment with unknown obstacles is addressed in this paper. Based on the simulated annealing algorithm, a flocking behaviour for mobile robots is achieved which converges to alignment while avoiding obstacles. Potential functions are designed to evaluate the positional relationship between robots and obstacles. Unlike the existing analytical method, simulated annealing algorithm is utilized to search the quasi-optimal position of robots in order to reduce the potential functions. Motion control law is designed to drive the robot move to the desired position at each sampling period. Experiments are implemented, and the results illustrate the effectiveness of the proposed flocking control method.
Flocking problems are studied and applied in many research fields, such as self-organized mobile sensor networks in [ Collision avoidance: avoid collisions with nearby flockmates Velocity matching: attempt to match velocity with nearby flockmates Flock centering: attempt to stay close to nearby flockmates
These behaviours are seen in astonishing amount of coordinated systems, which exhibit unbelievable efficient and robust coordination [
Booming-related work has been done worldwide in the last decades. Some works focus on the dynamic model of mobile robots [
In recent years, the flocking problem of mobile robots has become an attractive subject in the research field of the multiagent system and cooperative robots. In [
In practical applications, such as formulation of the mobile robot or surface vessels, the agent model is underactuated, and the kinematic motion is constricted with nonholonomic constraints. In our research project, AmigoBot is adopted as an
In this paper, a control method for the flocking problem of mobile robots is proposed. Simulated annealing (SA) algorithm is used to design a simple behaviour for each robot while flocking can be self-established. SA algorithm is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (e.g., the traveling salesman problem). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to alternatives such as gradient descent.
The paper is organized as follows. Section
The first model which is widely considered as a flocking agent is constructed in [
From the perspective of theoretical research, the dynamics of agents in flocking is also often modelled as a second-order linear system [
The other second-order linear system of the flocking agent is proposed in [
Different from the agent models proposed above which are treated with the linear system, the kinematic model of the mobile robot is much more complex. As shown in Figure
Mobile robot with sonar sensors. (a) AmigoBot. (b) Model of AmigoBot.
Unlike the models of (
For the differential wheel drive mobile robot, it has
Each mobile robot is considered as an
Potential function
The potential function of AmigoBot
Obstacles can be detected by AmigoBot with sonar sensors in an unknown environment. Define the position of the obstacle with
Define the projection of the position
Define the distance between robot
Define
With the aforementioned designed potential functions
For the flocking problem of the mobile robot in a complex environment with unknown obstacles, define the total potential function for robot
Obviously, if all the robots move towards the direction of the gradient descent of
Compared to other approximation methods, such as the Newton method, gradient descent method, and Levenberg–Marquardt method, SA can avoid being trapped in the local minimal in early iterations and is able to explore globally for better solutions in finite iterations [
The flocking control problem of mobile robots is considered as an approximation of the optimal solution of each
The pseudo-code of the random search method of
for Initialize else return
The initial position
Obviously, if
Once the quasi-optimal position
Define
Define
Define a candidate function
Define
The effectiveness of the proposed flocking control method is illustrated by experiments in MobileSim. MobileSim is software for simulating mobile robots and their environments, for debugging and experimentation with ARIA or other software that support mobile robot platforms. In this experiment, five AmigoBots are controlled to form a flocking centering state while avoiding the obstacles. The robots are connected by software with TCP ports from 8101 to 8105. Software is coded in VS2008. The data in the control process are stored in a text file at each sampling time, and the results are depicted in MATLAB figures.
The initial positions of the five AmigoBots are set with
The parameters in the method proposed above are designed as given in Table
Parameters in the flocking control method.
Variables | Value | |
---|---|---|
Potential function | 1000 mm | |
1000 mm | ||
Motion control | 0.0001 | |
0.003 | ||
SA algorithm | 100 | |
0.001 | ||
0.5 | ||
20 | ||
Step | 100 |
The initial and some intermediate processes of robots are shown in Figure
Experiment in MobileSim. (a)
The detailed traces of the five AmigoBots during the flocking process are depicted in Figure
Trajectories of robots.
Connection graph.
For the 10 connection graphs in Figure
The responses of potential functions
Potential function
Potential function
Figures
Orientation angles of robots.
Velocities of robots.
In this paper, the flocking behaviour of the mobile robot in an unknown environment with obstacles is designed via the heuristic search algorithm. With the potential functions defined for the
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This work was supported by the National Nature Science Foundation of China under Grant nos. 61203335 and 61603150.