Chaotic Mobility Models

In several mobility models, random processes are used to propose a non predictable behaviour. I propose to use chaotic systems to have both unpredictable trajectory and also moving patterns related to the chaotic dynamic.

Chaotic walk

Introduced by Iba & Shimonshi [IBA11], the authors name it chaotic walk because it only uses the logistic map

x_{n+1} = r x_n (1-x_n)

to determine the next angular direction \theta_{n} = 2 \pi x_{n} of an entity.

The logistic permits to obtain values x_n\in [0:1]. An entity move with a constant speed.

With r=4, the values obtained by the logistic map are not well distributed over the interval [0:1] and most of them are closed to the boundary. If we choose to build a mobility model, the logistic move, where the next position doesn’t depends on the previous one and only depends on the logistic map value, it leads to a mobility models oriented in one direction with variations: from the left to the right.


Fig. 1 - Eight agents performing the logistic move: they move mainly from left to right [1].

Let’s now consider the model proposed by [IBA11], the next angle is the sum of the previous one with the next one computed from the logistic map. Also, the authors use the parameter d as the number of decimal of the value x in the map.


Fig. 2 - Eight agents performing the chaotic walk [IBA11] (r=4 & d=100) [1].

Mobility model based on the Rössler system

Our work is based on the work of Kuiper & Nadjm-Tehrani [KUI06] where repulsive pheromones are used to cover an area in a Ant Colony Optimization method. The purpose of the CACOC mobility model (Chaotic Ant Colony Optimization to Coverage) is to combine a Ant Colony Optimization algorithm with chaotic dynamics [ROS18]. This have been performed using the Rössler system and it first return map to replace the random part dedicated to the exploration process.

Vid. 1 - CACOC mobility model in V-REP and in X-Y projection [ROS17].

Collision avoidance for CACOC

This work is extending CACOC by a Collision Avoidance (CA) mechanism and testing its efficiency in terms of area coverage by the UAV swarm. For this purpose, CACOC is used to com- pute UAV target waypoints which are tracked by model predictively controlled UAVs. The UAVs are represented by realistic motion models within the virtual robot experimentation platform (V-Rep). This environment is used to evaluate the performance of the proposed CACOC with CA algorithm in an area exploration scenario with 3 UAVs. Finally, its perfor- mance is analyzed using metrics.

Vid. 2 - Collision avoidance for CACOC mobility model in V-REP [DEN18].


[IBA11](1, 2, 3) T Iba & K Shimonishi, The Origin of Diversity: Thinking with Chaotic Walk, Unifying Themes in Complex Systems, 8, 447–461, 2011.
[ROS18]M. Rosalie, G. Danoy, S. Chaumette & P. Bouvry, Chaos-enhanced mobility models for multilevel swarms of UAVs, Swarm and Evolutionary Computation, 2018.
[ROS17]M. Rosalie, J. Dentler, G. Danoy, P. Bouvry, S. Kannan, M. A. Olivares-Mendez & H. Voos, Area exploration with a swarm of UAVs combining deterministic Chaotic Ant Colony Mobility with position MPC, In proc. of IEEE International Conference on Unmanned Aircraft Systems (ICUAS), 1392–1397, 2017.
[KUI06]E. Kuiper and S. Nadjm-Tehrani, Mobility Models for UAV Group Reconnaissance Applications, In Proc. of IEEE International Conference on Wireless and Mobile Communications (ICWMC), 2006
[DEN18]J. E. Dentler, M. Rosalie, G. Danoy, P. Bouvry, S. Kannan, M. A. Olivares-Mendez & H. Voos Collision avoidance effects on the mobility of a UAV swarm using Chaotic Ant Colony with Model Predictive Control Journal of Intelligent & Robotic Systems, 2018.


[1](1, 2) Simulation and figures are made with JBotSim Librairy.