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 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 this 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.

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A Survey on Aerial Swarm Robotics

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

In this paper, sliding-mode-control-based guidance laws to intercept stationary, constant-velocity, and maneuvering targets at a desired impact angle are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the missile's lateral acceleration to enforce terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. The conditions for capturability are also presented. In addition, by considering a three-degree-of-freedom linear-interceptor dynamic model and by following the procedure used to design a dynamic sliding-mode controller, the interceptor autopilot is designed as a simple static controller to track the lateral acceleration generated by the guidance law. Numerical simulation results are presented to validate the proposed guidance laws and the autopilot design for different initial engagement geometries and impact angles.

Sliding-Mode Guidance and Control for All-Aspect Interceptors with Terminal Angle Constraints

Linear quadratic guidance laws that explicitly enable imposing a predetermined intercept angle are presented. Two such guidance laws are derived, using optimal control and differential game theories, for arbitrary-order linear missile dynamics. The obtained guidance laws are dependent on the well-known zero-effort miss distance and on a new variable denoted zero-effort angle. It is shown that imposing the terminal angle constraint raises considerably the gains of the guidance laws. Theoretic conditions for the existence of a saddle-point solution in the differential game are also derived. These conditions show that imposing the terminal angle constraint requires a higher maneuverability advantage from the missile. The performance of the proposed guidance laws is investigated using a nonlinear two-dimensional simulation of the missile's lateral dynamics and relative kinematics, while assuming first-order dynamics for the target's evasive maneuvers. Using a Monte Carlo study, it is shown that, for the investigated problem, a target can be intercepted with a negligible miss distance and intercept angle error even when the target maneuvers and there are large initial heading errors.

Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle

G UIDANCE laws with terminal impact angle constraints are widely reported in the literature [1–7]. Proportional navigation guidance (PNG) has been used for deriving impact angle constrained guidance laws for stationary and moving targets. Lu et al. [8] have used PNG in an adaptive guidance law for a hypervelocity impact angle constrained hit at a stationary target. Satisfying impact angle constraint by varying the navigation constant N of the PNG is addressed by Ratnoo and Ghose [9]. In their work [9], a two-stage PNG law is proposed for achieving all impact angles against stationary targets in surface-to-surface engagements. A biased PNG (BPNG) law proposed by Kim et al. [3] has an extra term for annulling the terminal impact angle error together with the conventional line-of-sight rate term for the lateral acceleration command. BPNG law expands the capture region of existing guidance laws against moving targets. However, the performance of BPNG law deteriorates with tail-chase kinds of engagements. The problem of achieving all impact angles against moving targets is addressed here. The idea of a two-stage PNG law, proposed by Ratnoo and Ghose [9], is further investigated and developed for nonstationary nonmaneuvering targets. It should be noted that for different values of N, the PNG law results in a set of impact angles against a moving target. However, studies on classical PNG law [10] reveal that the value of N should be greater than a minimum value for the terminal lateral acceleration demand to be bounded. The achievable set of impact angles is derived for PNG law, with the values of N satisfying the previously mentioned constraint. To achieve the remaining impact angles, an orientation guidance scheme is proposed for the initial phase of the interceptor trajectory. The orientation guidance law is also PNG law, withN being a function of the initial engagement geometry. It is proven that, following the orientation trajectory, the interceptor can switch to N 3 and achieve any desired impact angle in a surface-to-surface engagement scenario.

Impact Angle Constrained Guidance Against Nonstationary Nonmaneuvering Targets

The paper proposes two linear quadratic guidance laws, which enable target interception while imposing a predetermined terminal intercept angle. Unlike previous solutions, which usually assume constant missile and target speeds, time-dependent known speed profiles of the adversaries are addressed. The guidance laws are derived for linear, arbitrary-order missile and target dynamics using optimal control and differential games theories. Specific closed-form results are provided for ideal missile and target dynamics with constant axial acceleration adversaries. The performance of the proposed guidance laws is investigated using a nonlinear two-dimensional simulation, and the results are compared to two state-of-the-art optimal control and differential-games-based guidance laws that can impose the intercept angle. It is shown that the proposed guidance laws can intercept the target with small miss distances and intercept angle errors and that they have better performance than the compared state-of-the-art guidance laws when the adversaries’ speeds vary. The selection of which guidance law to use depends on the scenario. When the target is predictable, the optimal-control-based guidance law is better suited; whereas when the target is intelligent, the differential-games-based guidance law is a more appropriate choice. 

Linear Quadratic Guidance Laws with Intercept Angle Constraints and Varying Speed Adversaries

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

https://ieeexplore.ieee.org/ielx7/87/4389040/09923626.pdf

Vitaly Shaferman

Papers

Linear Quadratic Guidance Laws with Intercept Angle Constraints and Varying Speed Adversaries

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application