21 research outputs found
Controllability and Stabilization of Kolmogorov Forward Equations for Robotic Swarms
abstract: Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the population of robots is represented as a continuum that evolves according to a mean-field model, which is directly designed such that the corresponding robot control policies produce target collective behaviours.
This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.
First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201
Intelligence, Creativity and Fantasy
UID/HIS/04666/2019
This is the 2nd volume of PHI series, published by CRC Press, the 4th published by CRC Press and the 5th volume of PHI proceedings.The texts presented in Proportion Harmonies and Identities (PHI) - INTELLIGENCE, CREATIVITY AND FANTASY were compiled with the intent to establish a multidisciplinary platform for the presentation, interaction and dissemination of research. The aim is also to foster the awareness and discussion on the topics of Harmony and Proportion with a focus on different visions relevant to Architecture, Arts and Humanities, Design, Engineering, Social and Natural Sciences, and their importance and benefits for the sense of both individual and community identity. The idea of modernity has been a significant motor for development since the Western Early Modern Age. Its theoretical and practical foundations have become the working tools of scientists, philosophers, and artists, who seek strategies and policies to accelerate the development process in different contexts.authorsversionpublishe
Cooperative task assignment for multiple vehicles
Multi-vehicle systems have been increasingly exploited to accomplish difficult and complex missions, where effective and efficient coordinations of the vehicles can greatly improve the team's performance. Motivated by need from practice, we study the multi-vehicle task assignment in various challenging environments. We first investigate the task assignment for multiple vehicles in a time-invariant drift field. The objective is to employ the vehicles to visit a set of target locations in the drift field while trying to minimize the vehicles' total travel time. Using optimal control theory, a path planning algorithm is designed to generate the time-optimal path for a vehicle to travel between any two prescribed locations in a drift field. The path planning algorithm provides the cost matrix for the target assignment, and generates routes once the target locations are assigned to the vehicles. Using tools from graph theory, a lower bound on the optimal solution is found, which can be used to measure the proximity of a solution from the optimal. We propose several clustering-based task assignment algorithms in which two of them guarantee that all the target locations will be visited within a computable maximal travel time, which is at most twice of the optimal when the cost matrix is symmetric. In addition, we extend the multi-vehicle task assignment study in a time-invariant drift field with obstacles. The vehicles have different capabilities, and each kind of vehicles need to visit a certain type of target locations; each target location might have the demand to be visited more than once by different kinds of vehicles. A path planning method has been designed to enable the vehicles to move between two prescribed locations in a drift field with the minimal time while avoiding obstacles. This task assignment problem is shown to be NP-hard, and a distributed task assignment algorithm has been designed, which can achieve near-optimal solutions to the task assignment problem. Furthermore, we study the task assignment problem in which multiple dispersed heterogeneous vehicles with limited communication range need to visit a set of target locations while trying to minimize the vehicles' total travel distance. Each vehicle initially has the position information of all the targets and of those vehicles that are within its limited communication range, and each target demands a vehicle with some specified capability to visit it. We design a decentralized auction algorithm which first employs an information consensus procedure to merge the local information carried by each communication-connected vehicle subnetwork. Then, the algorithm constructs conflict-free target assignments for the communication-connected vehicles, and guarantees that the total travel distance of the vehicles is at most twice of the optimal when the communication network is initially connected. In the end we exploit the precedence-constrained task assignment problem for a truck and a micro drone to deliver packages to a set of dispersed customers subject to precedence constraints that specify which customers need to be visited before which other customers. The truck is restricted to travel in a street network and the micro drone, restricted by its loading capacity and operation range, can fly from the truck to perform the last mile package deliveries. The objective is to minimize the time to serve all the customers respecting every precedence constraint. The problem is shown to be NP-hard, and a lower bound on the optimal time to serve all the customers is constructed by using tools from graph theory. Integrating with a topological sorting technique, several heuristic task assignment algorithms are constructed to solve the task assignment problem
Clustering-based algorithms for multi-vehicle task assignment in a time-invariant drift field
This paper studies the multi-vehicle task assignment problem where several dispersed vehicles need to visit a set of target locations in a time-invariant drift field while trying to minimize the total travel time. Using optimal control theory, we first design a path planning algorithm to minimize the time for each vehicle to travel between two given locations in the drift field. The path planning algorithm provides the cost matrix for the target assignment, and generates routes once the target locations are assigned to a vehicle. Then, we propose several clustering strategies to assign the targets, and we use two metrics to determine the visiting sequence of the targets clustered to each vehicle. Mainly used to specify the minimum time for a vehicle to travel between any two target locations, the cost matrix is obtained using the path planning algorithm, and is in general asymmetric due to time-invariant currents of the drift field. We show that one of the clustering strategies can obtain a min-cost arborescence of the asymmetric target vehicle graph where the weight of a directed edge between two vertices is the minimum travel time from one vertex to the other respecting the orientation. Using tools from graph theory, a lower bound on the optimal solution is found, which can be used to measure the proximity of a solution from the optimal. Furthermore, by integrating the target clustering strategies with the target visiting metrics, we obtain several task assignment algorithms. Among them, two algorithms guarantee that all the target locations will be visited within a computable maximal travel time, which is at most twice of the optimal when the cost matrix is symmetric. Finally, numerical simulations show that the algorithms can quickly lead to a solution that is close to the optimal
Proceedings of the International Micro Air Vehicles Conference and Flight Competition 2017 (IMAV 2017)
The IMAV 2017 conference has been held at ISAE-SUPAERO, Toulouse, France from Sept. 18 to Sept. 21, 2017. More than 250 participants coming from 30 different countries worldwide have presented their latest research activities in the field of drones. 38 papers have been presented during the conference including various topics such as Aerodynamics, Aeroacoustics, Propulsion, Autopilots, Sensors, Communication systems, Mission planning techniques, Artificial Intelligence, Human-machine cooperation as applied to drones
Decentralized Autonomous Navigation Strategies for Multi-Robot Search and Rescue
Use of multi-robot systems has many advantages over single robot systems in various applications. However, it comes with its own complexity and challenges. In this thesis, we try to improve the performance of existing approaches for search operations in multi-robot context. We propose three novel algorithms that are using a triangular grid pattern, i.e., robots certainly go through the vertices of a triangular grid during the search procedure. The main advantage of using a triangular grid pattern is that it is asymptotically optimal in terms of the minimum number of robots required for the complete coverage of an arbitrary bounded area. Therefore, using the vertices of this triangular grid coverage guarantees complete search of a region as well as shorter search duration.
We use a new topological map which is made and shared by robots during the search operation. We consider an area that is unknown to the robots a priori with an arbitrary shape, containing some obstacles. Unlike many current heuristic algorithms, we give mathematically rigorous proofs of convergence with probability 1 of the algorithms. The computer simulation results for the proposed algorithms are presented using a simulator of real robots and environment. We evaluate the performance of the algorithms via experiments with real Pioneer 3DX mobile robots. We compare the performance of our own algorithms with three existing algorithms from other researchers. The results demonstrate the merits of our proposed solution.
A further study on formation building with obstacle avoidance for a team of mobile robots is presented in this thesis. We propose a robust decentralized formation building with obstacle avoidance algorithm for a group of mobile robots to move in a defined geometric configuration. Furthermore, we consider a more complicated formation problem with a group of anonymous robots; these robots are not aware of their position in the final configuration and need to reach a consensus during the formation process. We propose a randomized algorithm for the anonymous robots that achieves the convergence to a desired configuration with probability 1. We also propose a novel obstacle avoidance rule, used in the formation building algorithm. A mathematically rigorous proof of the proposed algorithm is given. The performance and applicability of the proposed algorithm are confirmed by the computer simulation results
Decentralized Autonomous Navigation Strategies for Multi-Robot Search and Rescue
In this report, we try to improve the performance of existing approaches for
search operations in multi-robot context. We propose three novel algorithms
that are using a triangular grid pattern, i.e., robots certainly go through the
vertices of a triangular grid during the search procedure. The main advantage
of using a triangular grid pattern is that it is asymptotically optimal in
terms of the minimum number of robots required for the complete coverage of an
arbitrary bounded area. We use a new topological map which is made and shared
by robots during the search operation. We consider an area that is unknown to
the robots a priori with an arbitrary shape, containing some obstacles. Unlike
many current heuristic algorithms, we give mathematically proofs of convergence
of the algorithms. The computer simulation results for the proposed algorithms
are presented using a simulator of real robots and environment. We evaluate the
performance of the algorithms via experiments with real robots. We compare the
performance of our own algorithms with three existing algorithms from other
researchers. The results demonstrate the merits of our proposed solution. A
further study on formation building with obstacle avoidance for a team of
mobile robots is presented in this report. We propose a decentralized formation
building with obstacle avoidance algorithm for a group of mobile robots to move
in a defined geometric configuration. Furthermore, we consider a more
complicated formation problem with a group of anonymous robots; these robots
are not aware of their position in the final configuration and need to reach a
consensus during the formation process. We propose a randomized algorithm for
the anonymous robots that achieves the convergence to a desired configuration
with probability 1. We also propose a novel obstacle avoidance rule, used in
the formation building algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:1402.5188 by
other author
Spatial Formation Control
In this thesis, we study robust spatial formation control from several aspects. First, we study robust adaptive attitude synchronization for a network of rigid body agents using various attitude error functions defined on SO(3). Our results are particularly useful for networks with large initial attitude difference. We devise an adaptive geometric approach to cope with situations where the inertia matrices are not available for measurement. We use the Frobenius norm as a measure for the difference between the actual values of inertia matrices and their estimated values, to construct the individual adaptive laws of the agents. Compared to the previous methods for synchronization on SO(3) such as those which are based on quaternions, our proposed approach does not contain any attitude representation ambiguity. As the final part of our studies from the attitude synchronization aspect, we analyze robustness to external disturbances and unmodeled dynamics, and propose a method to attenuate such effects. Simulation results illustrate the effectiveness of the proposed approach. In the next part of the thesis, we study the distributed localization of the extremum point of unknown quadratic functions representing various physical or artificial signal potential fields. It is assumed that the value of such functions can be measured at each instant. Using high pass filtering of the measured signals, a linear parametric model is obtained for system identification. For design purposes, we add a consensus term to modify the identification subsystem. Next, we analyze the exponential convergence of the proposed estimation scheme using algebraic graph theory. In addition, we derive a distributed identifiability condition and use it for the construction of distributed extremum seeking control laws. In particular, we show that for a network of connected agents, if each agent contains a portion of the dithering signals, it is still possible to drive the system states to the extremum point provided that the distributed identifiability condition is satisfied. In the final part of this research, several robust control problems for general linear time invariant multi-agent systems are studied. We consider the robust consensus problem in the presence of unknown Lipschitz nonlinearities and polytopic uncertainties in the model of each agent. Next, this problem is solved in the presence of external disturbances. A set of control laws is proposed for the network to attain the consensus task and under the zero initial condition, achieves the desired H-infinity performance. We show that by implementing the modified versions of these control laws, it is possible to perform two-time scales formation control