This paper presents a novel method for controlling teams of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level planner that computes optimal state trajectories as velocity sequences, and a platform-specific low-level controller which ensures that these velocity sequences are met. The planning task is expressed as a centralized path-integral control problem, for which optimal control computation corresponds to a probabilistic inference problem that can be solved by efficient sampling methods. Through simulation we show that our SOC approach (a) has significant benefits compared to deterministic control and other SOC methods in multimodal problems with noise-dependent optimal solutions, (b) is capable of controlling a large number of platforms in real-time, and (c) yields collective emergent behaviour in the form of flight formations. Finally, we show that our approach works for real platforms, by controlling a team of three quadrotors in outdoor conditions.
In outdoor conditions, motion capture is difficult and Global Positioning System (GPS) is used instead. Existing control approaches are typically either based on Reynolds flocking @cite_13 @cite_11 @cite_10 @cite_1 or flight formation @cite_8 @cite_0 . In Reynolds flocking, each agent is considered a point mass that obeys simple and distributed rules: separate from neighbors, align with the average heading of neighbors and steer towards neighborhood centroid to keep cohesion. Flight formation control is typically modeled using graphs, where every node is an agent that can exchange information with all or several agents. Velocity and or position coordination is usually achieved using consensus algorithms.
@cite_13 @cite_8 @cite_1 @cite_0 @cite_10 @cite_11
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In flocking, a swarm of robots moves cohesively in a common direction. Traditionally, flocking is realized using two main control rules: proximal control, which controls the cohesion of the swarm using local range-and bearing information about neighboring robots; and alignment control, which allows the robots to align in a common direction and uses more elaborate sensing mechanisms to obtain the orientation of neighboring robots. So far, limited attention has been given to motion control, used to translate the output of these two control rules into robot motion. In this paper, we propose a novel motion control method: magnitude-dependent motion control (MDMC). Through simulations and real robot experiments, we show that, with MDMC, flocking in a random direction is possible without the need for alignment control and for robots having a preferred direction of travel. MDMC has the advantage to be implementable on very simple robots that lack the capability to detect the orientation of their neighbors. In addition, we introduce a small proportion of robots informed about a desired direction of travel. We compare MDMC with a motion control method used in previous robotics literature, which we call magnitude-independent motion control (MIMC), and we show that the swarms can travel longer distances in the desired direction when using MDMC instead of MIMC. Finally, we systematically study flocking under various conditions: with or without alignment control, with or without informed robots, with MDMC or with MIMC. In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called spl alpha -lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or spl alpha -agents, and virtual agents associated with spl alpha -agents called spl beta - and spl gamma -agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms. An approach for coordination and control of 3D heterogeneous formations of unmanned aerial and ground vehicles under hawk-eye-like relative localization is presented in this paper. The core of the method lies in the use of visual top-view feedback from flying robots for the stabilization of the entire group in a leader-follower formation. We formulate a novel model predictive control-based methodology for guiding the formation. The method is employed to solve the trajectory planning and control of a virtual leader into a desired target region. In addition, the method is used for keeping the following vehicles in the desired shape of the group. The approach is designed to ensure direct visibility between aerial and ground vehicles, which is crucial for the formation stabilization using the hawk-eye-like approach. The presented system is verified in numerous experiments inspired by search-and-rescue applications, where the formation acts as a searching phalanx. In addition, stability and convergence analyses are provided to explicitly determine the limitations of the method in real-world applications. A team of three Unmanned Aerial Vehicles (UAVs) accomplishes a line abreast, triangular and cross formation based on high-level Linear Model Predictive Control (LMPC). All flight tests respect Reynold's rules of flocking, where the UAVs avoid collisions with nearby flockmates, attempt to match velocity of other team members and attempt to stay close to other flockmates. A linear system identification model is at the base of the error dynamics describing the formation control algorithm. The main contribution of this paper lies in the use of LMPC to implement multiple formations on UAVs in simulation and using the Qball-X4 quadrotor.