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

A cooperative guidance law, for a defender missile protecting an aerial target from an incoming homing missile, is presented. The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile. Fusion of measurements from both the defender missile and protected aircraft is performed. A matched defender’s missile guidance law is optimized to the identified homing missile guidance law. It utilizes cooperation between the aerial target and the defender missile. The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile. Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender. The estimator and guidance law are combined in a multiple model adaptive control configuration. Simulation results show that combining the estimations with the proposed optimal guidance law, that utilizes cooperation between the defending missile and protected target, yields hit-to-kill closed loop performance with very low control effort. This facilitates the use of relatively small defending missiles to protect aircrafts from homing missiles.

Cooperative Multiple-Model Adaptive Guidance for an Aircraft Defending Missile

Optimal control-based cooperative guidance laws, which enforce at intercept a relative geometry in between a group of missiles and a single maneuvering target, are presented. An example scenario of interest is that of intercepting a high-value target (such as a ballistic missile) by a team of cooperating interceptors arriving from different directions. The problem is posed in the linear quadratic framework, and closed-form analytic solutions are obtained for any team size with any linear missile dynamics. The performance of the cooperative guidance laws is investigated using a nonlinear two-dimensional simulation of the missiles’ lateral dynamics and relative kinematics. It is shown that cooperatively imposing a relative intercept angle between the missiles provides substantially better results than when each missile independently enforces, using a one-on-one strategy, a preselected intercept angle that satisfies the relative intercept requirement. It is also shown that the missiles’ acceleration requirem...

Cooperative Optimal Guidance Laws for Imposing a Relative Intercept Angle

The problem of autonomous tracking of a ground moving target in an urban terrain is studied. In the investigated scenario, the target is tracked from multiple unmanned aerial vehicles using gimballed or body-fixed sensors under the constraints of terrain occlusions and airspace limitations. Information regarding the occlusions may be available a priori from a database or may be provided to the system by the operator based on his understanding of the environment. To ensure flyable trajectories, the unmanned aerial vehicles' dynamic constrains must be taken into account. A methodology is proposed for solving in real time a general class of such problems by casting the tracking task as a cooperative motion planning problem. Because of the computational complexity of the problem, a stochastic search method (genetic algorithm) is proposed for finding in real time monotonically improving solutions. An important attribute of the proposed solution approach is its scalability and, consequently, applicability to large-sized problems. For testing the algorithm, it was implemented in a high-fidelity simulation test bed using a visual database of an actual city. The viability of using the algorithm is shown using a Monte Carlo study. It is envisioned that automating this part of a ground moving target tracking problem will considerably reduce operators' workload and dramatically improve mission performance in such real-life problems.

Unmanned Aerial Vehicles Cooperative Tracking of Moving Ground Target in Urban Environments

A cooperative guidance law for a team of interceptors trying to intercept, from multiple directions, an evading target is proposed. An example scenario of interest is that of intercepting an aerial...

Vitaly Shaferman

Papers

Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle

Cooperative Multiple-Model Adaptive Guidance for an Aircraft Defending Missile

Cooperative Optimal Guidance Laws for Imposing a Relative Intercept Angle

Unmanned Aerial Vehicles Cooperative Tracking of Moving Ground Target in Urban Environments

Cooperative Differential Games Guidance Laws for Imposing a Relative Intercept Angle