Gareth Basset

Sequential virtual motion camouflage method for nonlinear constrained optimal trajectory control

Nonlinear constrained optimal trajectory planning is a challenging and fundamental area of research. This paper proposes bio-inspired fast-time approaches for this type of problems based on the inspiration drawn from the natural phenomenon known as the motion camouflage. Two algorithms are proposed: the virtual motion camouflage (VMC) subspace method and the sequential VMC method. As a hybrid approach, the sequential VMC method works through a two-step structure in each iteration. First, the VMC subspace method will solve for an optimal solution over a selected subspace. Second, an algorithm consisting of a linear programming and a line search will vary the subspace so that the next VMC subspace result will be guaranteed not to be worse than that of the current step. The dimension and time complexities of the algorithms will be analyzed, and the optimality of the solution via the sequential VMC approach will be studied. Through the VMC approaches, the state and control variables in the kinematics or dynamics models of vehicles in the selected subspace can be represented by a single degree-of-freedom vector, called the path control parameter vector. The reduction in dimension and no involvement of equality constraints will in practice make the convergence faster and easier, and a much smaller computational cost is expected. Two simulation examples, the Breakwell problem and a minimum time robot obstacle avoidance problem with different numbers of obstacles, are used to demonstrate the capabilities of the algorithms.

Brief paper: Virtual motion camouflage based phantom track generation through cooperative electronic combat air vehicles

As an example of complex cooperative missions, coherent phantom track generation through controlling multiple electronic combat air vehicles is currently an area of great interest to the defense agency for the purpose of deceiving a radar network. However, it has been a challenge to design optimal coherent trajectories for this type of problems due to the high dimensionality and kinematic, dynamics, and geometric constraints. This paper describes how an interesting bio-inspired motion strategy can be used to design real-time trajectories for a (1) feasible constant speed coherent mission, (2) maximum-duration constant speed coherent mission, and (3) optimal trajectory mission for general cases.

Pre and Post Optimality Checking of the Virtual Motion Camouflage based Nonlinear Constrained Subspace Optimal Control

Nonlinear constrained trajectory optimization remains an active field of research. Current popular methods end up with either solving a classical multi-dimensional two-point boundary value problem or a high dimensional nonlinear programming problem. Inspired by the motion camouflage phenomenon of insects like dragonflies, recently the authors proposed a subspace optimization method, the virtual motion camouflage method, in order to reduce the problem dimension. Thus the computational cost experienced in the widely used direct collocation and nonlinear programming methods can be reduced. The solution found through this approach is in the feasible region however the optimality of the solution is not guaranteed automatically in the original full search space. In this paper, two optimality checking ways extended from the Karush-Kuhn-Tucker necessary condition are proposed. The pre-optimality checking is proposed to judge the selection of the virtual prey motion and the reference point, while a post-optimality checking is suggested to test the solution obtained from the virtual motion camouflage method in the original search space. Two numerical examples are used to illustrate the capabilities of the new subspace optimal control algorithm.

Bio-Inspired Rendezvous Strategies and Respondent Detections

In nature, many biological species have devised simple yet effective motion strategies that help them with a variety of tasks, such as foraging and mating. One such phenomenon has been observed in hoverflies, in which a male hoverfly moves in a certain path and appears stationary from the viewpoint of a moving female hoverfly. The use of this new bio-inspired strategy has recently been considered for rendezvous tasks in space situation-awareness missions. In this paper, the feasibilities of applying such a rendezvous strategy to free-flying (i.e., zero applied control acceleration) space vehicles and the respondent detections of such motion strategies to prevent orbital collisions are investigated in the local vertical and local horizontal frame. Algorithms for nontrivial free-flying scenarios are derived for both fixed and free-flying spacecraft. The extended Kalman filter is designed to demonstrate the ability to detect and monitor these types of rendezvous motions.

Real-Time Optimal Coherent Phantom Track Generation via the Virtual Motion Camouflage Approach

Coherent phantom track generation through controlling a group of electronic combat air vehicles is currently an area of great interest to the defense agency for the purpose of deceiving a radar network. However, generating an optimal or even feasible coherent phantom trajectory in real-time is challenging due to the high dimensionality of the problem and severe geometric constraints. This problem becomes even more difficult to solve when realistic kinematic and 6DOF dynamic constraints are considered. In this paper, the bio-inspired virtual motion camouflage based trajectory planning methodology, augmented with the derived early termination condition, is investigated to solve this constrained collaborative trajectory planning problem in two approaches: centralized and decentralized. In the centralized approach, one optimization loop is used to solve for the coherent trajectories for both phantom and electronic combat air vehicles. The virtual motion camouflage based formulation can help to dramatically reduce the problem dimension. In the decentralized approach, two optimization loops are designed. The first loop finds feasible phantom tracks based on the early termination condition and the equality and inequality constraints of the phantom track. Then the second loop uses the virtual motion camouflage based method to solve for the optimal electronic combat air vehicle trajectories based on the feasible phantom tracks obtained in the first loop. For both approaches, necessary conditions have been applied so that the initial and final velocities of the phantom and electronic combat air vehicles are guaranteed to be coherent. Through the proposed bio-inspired method, the dynamics models of the coherent pair of the phantom and actual vehicles can be represented by a single-degree-of-freedom vector, called the path control parameter vector. Thus a fast optimal phantom track design can be achieved. The fact that fewer equality constraints are involved in solving the formulated nonlinear programming problem will further make the convergence easier. Optimal solutions have been found in both centralized and decentralized simulations for several cases with different numbers of electronic combat air vehicles and varying numbers of discretization nodes. It is demonstrated that the decentralized approach can solve the problem much faster than the centralized one. Furthermore, the computational cost in the decentralized approach remains roughly the same for the cases when different numbers of nodes and different numbers of electronic combat air vehicles are involved. In comparison, the computational cost in the centralized approach increases dramatically when the number of nodes and/or the number of electronic combat air vehicles increases. It is concluded that the virtual motion camouflage based decentralized approach is appropriate for real-time implementation.

Virtual motion camouflage based phantom track generation through cooperative electronic combat air vehicles

As an example of complex cooperative missions, coherent phantom track generation through controlling multiple electronic combat air vehicles is currently an area of great interest to the defense agency for the purpose of deceiving a radar network. However, it has been a challenge to design optimal coherent trajectories for this type of problems due to the high dimensionality and kinematic, dynamics, and geometric constraints. This paper describes how an interesting bio-inspired motion strategy can be used to design real-time trajectories for a (1) feasible constant speed coherent mission, (2) maximum-duration constant speed coherent mission, and (3) optimal trajectory mission for general cases.

Optimal coherent phantom track design using virtual motion camouflage

The virtual motion camouflage based trajectory planning methodology, augmented with the derived early termination conditions, is proposed to design the optimal collaborative trajectories for electronic combat air vehicles in constructing a coherent phantom track. In this problem, a realistic 6DOF dynamics model and severe state, control, control rate, and geometric constraints are all considered. An innovative virtual motion camouflage based method is applied to solve the inner-loop optimization problem in a very quick fashion. For the outer-loop, the early termination conditions are used to reduce the computational time by not executing the inner-loop optimization if these conditions are violated by the guessed phantom track. The early termination conditions include the necessary conditions derived based on the motion camouflage steering law and feasibility conditions derived according to the state, control, and control rate constraints.

Analytical neighboring optimal guidance to finite horizon linear quadratic tracking problems

In this paper, a new approach to solving finite horizon linear quadratic tracking problems is proposed. An analytical means is derived based on the virtual motion camouflage concept, and pseudospectral discretization and differential inclusion techniques. The method avoids several disadvantages of classic approaches by avoiding backward propagation and satisfying the boundary conditions exactly. The solution requires only a single matrix inversion and a numerical example is provided to show the effectiveness of the algorithm.

Fast trajectory planning via the B-spline augmented virtual motion camouflage approach

Nonlinear constrained optimal trajectory control is an important and fundamental area of research that continues to advance. This paper proposes an improved version of the bio-inspired virtual motion camouflage (VMC) method, which is based on the natural phenomenon of motion camouflage. Currently, the VMC method offers fast solutions that fall close to the optimal solution, but the solution optimality is affected by a selected and fixed search space that is defined by a fixed polynomial type prey motion. To increase the flexibility of the search space and thus improve the solution optimality, this paper proposes using B-spline curves to represent the prey motion, in which the control points and thus the prey motion can be optimized. It is expected that the proposed B-spline augmented VMC method will improve the solution optimality without sacrificing the CPU time too much. A minimum time obstacle avoidance robot problem will be simulated to demonstrate the capabilities of the algorithm.

Feasibility and detection of a bio-inspired approach for space situational awareness

In nature, many biological species have devised motion strategies that help them with a variety of tasks, such as mating and foraging. One such phenomenon that has been recently studied in hoverflies involves a moving male hoverfly that conceals its motion from the viewpoint of a moving female hoverfly. The use of this bio-inspired strategy has also recently been considered in the context of Space Situational Awareness. In this paper, the feasibilities of applying the bio-inspired technique to free flying space vehicles are investigated. Furthermore, the detectability of the motion strategy is studied. Both the feasibilities and the detectability are investigated in the local vertical and local horizontal frame.