Abstract-Concurrent synchronization is a regime where diverse groups of fully synchronized dynamic systems stably coexist. We study global exponential synchronization and concurrent synchronization in the context of Lagrangian systems control. In a network constructed by adding diffusive couplings to robot manipulators or mobile robots, a decentralized tracking control law globally exponentially synchronizes an arbitrary number of robots, and represents a generalization of the average consensus problem. Exact nonlinear stability guarantees and synchronization conditions are derived by contraction analysis. The proposed decentralized strategy is further extended to adaptive synchronization and partialstate coupling.

Abstract-The use of aerial swarms to solve real-world problems has been increasing steadily, accompanied by falling prices and improving performance of communication, sensing, and processing hardware. The commoditization of hardware has reduced unit costs, thereby lowering the barriers to entry to the field of aerial swarm robotics. A key enabling technology for swarms is the family of algorithms that allow the individual members of the swarm to communicate and allocate tasks amongst themselves, plan their trajectories, and coordinate their flight in such a way that the overall objectives of the swarm are achieved efficiently. These algorithms, often organized in a hierarchical fashion, endow the swarm with autonomy at every level, and the role of a human operator can be reduced, in principle, to interactions at a higher level without direct intervention. This technology depends on the clever and innovative application of theoretical tools from control and estimation. This paper reviews the state of the art of these theoretical tools, specifically focusing on how they have been developed for, and applied to, aerial swarms. Aerial swarms differ from swarms of ground-based vehicles in two respects: they operate in a three-dimensional (3-D) space, and the dynamics of individual vehicles adds an extra layer of complexity. We review dynamic modeling and conditions for stability and controllability that are essential in order to achieve cooperative flight and distributed sensing. The main sections of the paper focus on major results covering trajectory generation, task allocation, adversarial control, distributed sensing, monitoring, and mapping. Wherever possible, we indicate how the physics and subsystem technologies of aerial robots are brought to bear on these individual areas.

This paper presents a decentralized, model predictive control algorithm for the optimal guidance and reconfiguration of swarms of spacecraft composed of hundreds to thousands of agents with limited capabilities. In previous work, J 2-invariant orbits have been found to provide collision-free motion for hundreds of orbits in a low Earth orbit. This paper develops real-time optimal control algorithms for the swarm reconfiguration that involve transferring from one J 2-invariant orbit to another while avoiding collisions and minimizing fuel. The proposed model predictive control-sequential convex programming algorithm uses sequential convex programming to solve a series of approximate path planning problems until the solution converges. By updating the optimal trajectories during the reconfiguration, the model predictive control algorithm results in decentralized computations and communication between neighboring spacecraft only. Additionally, model predictive control reduces the horizon of the convex optimizations, which reduces the run time of the algorithm. Multiple time steps, time-varying collision constraints, and communication requirements are developed to guarantee stability, feasibility, and robustness of the model predictive control-sequential convex programming algorithm.

Precise near-ground trajectory control is difficult for multi-rotor drones, due to the complex aerodynamic effects caused by interactions between multi-rotor airflow and the environment. Conventional control methods often fail to properly account for these complex effects and fall short in accomplishing smooth landing. In this paper, we present a novel deeplearning-based robust nonlinear controller (Neural-Lander) that improves control performance of a quadrotor during landing. Our approach combines a nominal dynamics model with a Deep Neural Network (DNN) that learns high-order interactions. We apply spectral normalization (SN) to constrain the Lipschitz constant of the DNN. Leveraging this Lipschitz property, we design a nonlinear feedback linearization controller using the learned model and prove system stability with disturbance rejection. To the best of our knowledge, this is the first DNNbased nonlinear feedback controller with stability guarantees that can utilize arbitrarily large neural nets. Experimental results demonstrate that the proposed controller significantly outperforms a Baseline Nonlinear Tracking Controller in both landing and cross-table trajectory tracking cases. We also empirically show that the DNN generalizes well to unseen data outside the training domain.

This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the Swarm Assignment and Trajectory Optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.

This paper presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on oscillator phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. Although the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework.

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This paper presents a new design approach to nonlinear observers for Itï¿oe stochastic nonlinear systems with guaranteed stability. A stochastic contraction lemma is presented which is used to analyze incremental stability of the observer. A bound on the mean-squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity. The observer design is based on a non-unique state-dependent coefficient (SDC) form, which parametrizes the nonlinearity in an extended linear form. The observer gain synthesis algorithm, called linear matrix inequality statedependent algebraic Riccati equation (LMI-SDARE), is presented. The LMI-SDARE uses a convex combination of multiple SDC parametrizations. An optimization problem with statedependent linear matrix inequality (SDLMI) constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances. Two variations of LMI-SDARE algorithm are also proposed. One of them named convex state-dependent Riccati equation (CSDRE) uses a chosen convex combination of multiple SDC matrices; and the other named Fixed-SDARE uses constant SDC matrices that are pre-computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre-computed by a convex LMI optimization problem. A connection between contraction analysis and L2 gain of the nonlinear system is established in the presence of noise and disturbances. Results of simulation show superiority of the LMI-SDARE algorithm to the extended Kalman filter (EKF) and state-dependent differential Riccati equation (SDDRE) filter.