Hierarchical Decentralized LQR Control for Formation-Keeping of Cooperative Mobile Robots in Material Transport Tasks

This study provides a formation-keeping method based on consensus for mobile robots used in cooperative transport applications that prevents accidental damage to the objects being carried. The algorithm can be used to move both rigid and elastic materials, where the desired formation geometry is predefined. The cooperative mobile robots must maintain formation even when encountering unknown obstacles, which are detected using each robot's on-board sensors. Local actions would then be taken by the robot to avoid collision. However, the obstacles may not be detected by other robots in the formation due to line-of-sight or range limitations. Without sufficient communication or coordination between robots, local collision avoidance protocols may lead to the loss of formation geometry. This problem is most notable when the object being transported is deformable, which reduces the physical force interaction between robots when compared to rigid materials. Thus, a decentralized, hierarchical LQR control scheme is proposed that guarantees formation-keeping despite local collision avoidance actions, for both rigid and elastic objects. Representing the cooperative robot formation using multi-agent system framework, graph Laplacian potential and Lyapunov stability analysis are used to guarantee tracking performance and consensus. The effectiveness and scalability of the proposed method are illustrated by computer simulations of line (2 robots) and quadrilateral (4 robots) formations. Different communication topologies are evaluated and provide insights into the minimum bandwidth required to maintain formation consensus

Continuum Deformation of a Multiple Quadcopter Payload Delivery Team without Inter-Agent Communication

This paper proposes continuum deformation as a strategy for controlling the collective motion of a multiple quadcopter system (MQS) carrying a common payload. Continuum deformation allows expansion and contraction of inter-agent distances in a 2D motion plane to follow desired motions of three team leaders. The remaining quadcopter followers establish the desired continuum deformation only by knowing leaders positions at desired sample time waypoints without the need for inter-agent communication over the intermediate intervals. Each quadcopter applies a linear-quadratic-Gaussian (LQG) controller to track the desired trajectory given by the continuum deformation in the presence of disturbance and measurement noise. Results of simulated cooperative aerial payload transport in the presence of uncertainty illustrate the application of continuum deformation for coordinated transport through a narrow channel

Estimation and stability of nonlinear control systems under intermittent information with applications to multi-agent robotics

This dissertation investigates the role of intermittent information in estimation and control problems and applies the obtained results to multi-agent tasks in robotics. First, we develop a stochastic hybrid model of mobile networks able to capture a large variety of heterogeneous multi-agent problems and phenomena. This model is applied to a case study where a heterogeneous mobile sensor network cooperatively detects and tracks mobile targets based on intermittent observations. When these observations form a satisfactory target trajectory, a mobile sensor is switched to the pursuit mode and deployed to capture the target. The cost of operating the sensors is determined from the geometric properties of the network, environment and probability of target detection. The above case study is motivated by the Marco Polo game played by children in swimming pools. Second, we develop adaptive sampling of targets positions in order to minimize energy consumption, while satisfying performance guarantees such as increased probability of detection over time, and no-escape conditions. A parsimonious predictor-corrector tracking filter, that uses geometrical properties of targets\u27 tracks to estimate their positions using imperfect and intermittent measurements, is presented. It is shown that this filter requires substantially less information and processing power than the Unscented Kalman Filter and Sampling Importance Resampling Particle Filter, while providing comparable estimation performance in the presence of intermittent information. Third, we investigate stability of nonlinear control systems under intermittent information. We replace the traditional periodic paradigm, where the up-to-date information is transmitted and control laws are executed in a periodic fashion, with the event-triggered paradigm. Building on the small gain theorem, we develop input-output triggered control algorithms yielding stable closed-loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise environment, the developed algorithm yields stable, asymptotically stable, and Lp-stable (with bias) closed-loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on Lp-stability are presented. Prediction of a triggering event is achieved by employing Lp-gains over a finite horizon in the small gain theorem. By resorting to convex programming, a method to compute Lp-gains over a finite horizon is devised. Next, we investigate optimal intermittent feedback for nonlinear control systems. Using the currently available measurements from a plant, we develop a methodology that outputs when to update the control law with new measurements such that a given cost function is minimized. Our cost function captures trade-offs between the performance and energy consumption of the control system. The optimization problem is formulated as a Dynamic Programming problem, and Approximate Dynamic Programming is employed to solve it. Instead of advocating a particular approximation architecture for Approximate Dynamic Programming, we formulate properties that successful approximation architectures satisfy. In addition, we consider problems with partially observable states, and propose Particle Filtering to deal with partially observable states and intermittent feedback. Finally, we investigate a decentralized output synchronization problem of heterogeneous linear systems. We develop a self-triggered output broadcasting policy for the interconnected systems. Broadcasting time instants adapt to the current communication topology. For a fixed topology, our broadcasting policy yields global exponential output synchronization, and Lp-stable output synchronization in the presence of disturbances. Employing a converse Lyapunov theorem for impulsive systems, we provide an average dwell time condition that yields disturbance-to-state stable output synchronization in case of switching topology. Our approach is applicable to directed and unbalanced communication topologies.\u2

Novel probabilistic and distributed algorithms for guidance, control, and nonlinear estimation of large-scale multi-agent systems

Multi-agent systems are widely used for constructing a desired formation shape, exploring an area, surveillance, coverage, and other cooperative tasks. This dissertation introduces novel algorithms in the three main areas of shape formation, distributed estimation, and attitude control of large-scale multi-agent systems. In the first part of this dissertation, we address the problem of shape formation for thousands to millions of agents. Here, we present two novel algorithms for guiding a large-scale swarm of robotic systems into a desired formation shape in a distributed and scalable manner. These probabilistic swarm guidance algorithms adopt an Eulerian framework, where the physical space is partitioned into bins and the swarm's density distribution over each bin is controlled using tunable Markov chains. In the first algorithm - Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC) - each agent determines its bin transition probabilities using a time-inhomogeneous Markov chain that is constructed in real-time using feedback from the current swarm distribution. This PSG-IMC algorithm minimizes the expected cost of the transitions required to achieve and maintain the desired formation shape, even when agents are added to or removed from the swarm. The algorithm scales well with a large number of agents and complex formation shapes, and can also be adapted for area exploration applications. In the second algorithm - Probabilistic Swarm Guidance using Optimal Transport (PSG-OT) - each agent determines its bin transition probabilities by solving an optimal transport problem, which is recast as a linear program. In the presence of perfect feedback of the current swarm distribution, this algorithm minimizes the given cost function, guarantees faster convergence, reduces the number of transitions for achieving the desired formation, and is robust to disturbances or damages to the formation. We demonstrate the effectiveness of these two proposed swarm guidance algorithms using results from numerical simulations and closed-loop hardware experiments on multiple quadrotors. In the second part of this dissertation, we present two novel discrete-time algorithms for distributed estimation, which track a single target using a network of heterogeneous sensing agents. The Distributed Bayesian Filtering (DBF) algorithm, the sensing agents combine their normalized likelihood functions using the logarithmic opinion pool and the discrete-time dynamic average consensus algorithm. Each agent's estimated likelihood function converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. Using a new proof technique, the convergence, stability, and robustness properties of the DBF algorithm are rigorously characterized. The explicit bounds on the time step of the robust DBF algorithm are shown to depend on the time-scale of the target dynamics. Furthermore, the DBF algorithm for linear-Gaussian models can be cast into a modified form of the Kalman information filter. In the Bayesian Consensus Filtering (BCF) algorithm, the agents combine their estimated posterior pdfs multiple times within each time step using the logarithmic opinion pool scheme. Thus, each agent's consensual pdf minimizes the sum of Kullback-Leibler divergences with the local posterior pdfs. The performance and robust properties of these algorithms are validated using numerical simulations. In the third part of this dissertation, we present an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feed-forward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees global exponential convergence of tracking errors with finite-gain Lp stability in the presence of modeling uncertainties and disturbances, and reduces the resultant disturbance torque. Further, this control law permits the use of any attitude representation and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law, because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional-derivative based reference trajectory, because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control law is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept. The new algorithms proposed in this dissertation will facilitate the development of versatile autonomous multi-agent systems that are capable of performing a variety of complex tasks in a robust and scalable manner

Intelligent Autonomous Decision-Making and Cooperative Control Technology of High-Speed Vehicle Swarms

This book is a reprint of the Special Issue “Intelligent Autonomous Decision-Making and Cooperative Control Technology of High-Speed Vehicle Swarms”,which was published in Applied Sciences

Hierarchical Decentralized LQR Control for Formation-Keeping of Cooperative Mobile Robots in Material Transport Tasks

This study provides a formation-keeping method based on consensus for mobile robots used in cooperative transport applications that prevents accidental damage to the objects being carried. The algorithm can be used to move both rigid and elastic materials, where the desired formation geometry is predefined. The cooperative mobile robots must maintain formation even when encountering unknown obstacles, which are detected using each robot's on-board sensors. Local actions would then be taken by the robot to avoid collision. However, the obstacles may not be detected by other robots in the formation due to line-of-sight or range limitations. Without sufficient communication or coordination between robots, local collision avoidance protocols may lead to the loss of formation geometry. This problem is most notable when the object being transported is deformable, which reduces the physical force interaction between robots when compared to rigid materials. Thus, a decentralized, hierarchical LQR control scheme is proposed that guarantees formation-keeping despite local collision avoidance actions, for both rigid and elastic objects. Representing the cooperative robot formation using multi-agent system framework, graph Laplacian potential and Lyapunov stability analysis are used to guarantee tracking performance and consensus. The effectiveness and scalability of the proposed method are illustrated by computer simulations of line (2 robots) and quadrilateral (4 robots) formations. Different communication topologies are evaluated and provide insights into the minimum bandwidth required to maintain formation consensus