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A proposed mission extension for LISA Pathfinder involved redirecting the probe to the Sun–Earth gravitational saddle point. Realistic models for both space and ground segments were used to carry out a number of analyses for trajectory design, orbit determination, and navigation cost. In this work, we present the methods that allow assessing the feasibility of flying general limited-control-authority spacecraft in highly nonlinear dynamics, and in particular of the proposed mission extension in a statistically reliable approach. Solutions for transfers from the Sun–Earth L 1 and L 2 to the saddle point are shown, which feature very low Δ v consumption, from few centimeters per second to 10 m/s. The analysis is then specialized to the case of LISA Pathfinder, for which several solutions are presented. This work gives evidence that LISA Pathfinder might have been able to fly-through the saddle point, provided initial tracking errors within 10 km in each position component and 0.1 m/s in each velocity component. A critical discussion on the opportunistic mission extension is eventually made. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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 the optimal or even feasible coherent trajectories for this type of problem due to the high dimensionality and the strong coupling between the phantom and actual vehicles. This problem becomes even more difficult to solve when realistic kinematic, dynamics, and geometric constraints in a three-degree-of-freedom formation have to be considered. 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. The proposed method will dramatically reduce the dimension of the problem and thus real-time optimal trajectory design can be achieved. Also the fact that fewer equality constraints are involved in solving the formulated nonlinear programming will make the convergence a lot easier. [ABSTRACT FROM AUTHOR]

Abstract: A design technique for a near optimal, Earth–Moon transfer trajectory using continuous variable low thrust is proposed. For the Earth–Moon transfer trajectory, analytical and numerical methods are combined to formulate the trajectory optimization problem. The basic concept of the proposed technique is to utilize analytically optimized solutions when the spacecraft is flying near a central body where the transfer trajectories are nearly circular shaped, and to use a numerical optimization method to match the spacecraft’s states to establish a final near optimal trajectory. The plasma thruster is considered as the main propulsion system which is currently being developed for crewed/cargo missions for interplanetary flight. The gravitational effects of the 3rd body and geopotential effects are included during the trajectory optimization process. With the proposed design technique, Earth–Moon transfer trajectory is successfully designed with the plasma thruster having a thrust direction sequence of “fixed-varied-fixed” and a thrust acceleration sequence of “constant-variable-constant”. As this strategy has the characteristics of a lesser computational load, little sensitivity to initial conditions, and obtaining solutions quickly, this method can be utilized in the initial scoping studies for mission design and analysis. Additionally, derived near optimal trajectory solution can be used as for initial trajectory solution for further detailed optimization problem. The demonstrated results will give various insights into future lunar cargo trajectories using plasma thrusters with continuous variable low thrust, establishing approximate costs as well as trajectory characteristics. [Copyright &y& Elsevier]

It is well-known that helicopters descending fast may enter the so-called Vortex Ring State (VRS), a region in the velocity space where the blade's lift differs significantly from regular regions and high amplitude fluctuations are often present. These fluctuations may lead to instability and, therefore, this region is avoided, typically by increasing the horizontal speed. This paper researches this phenomenon in the context of small-scale quadcopters. The region corresponding to the VRS is identified by combining first-principles modeling and wind-tunnel experiments. Moreover, we propose that the so-called Windmill-Brake State (WBS) or autorotation region should also be avoided for quadcopters, which is not necessarily the case for helicopters. A model is proposed for the velocity constraints that the quadcopter must meet in order to avoid these regions. Then, the problem of designing optimal time descent trajectories that avoid the VRS and WBS regions is tackled. Finally, the optimal trajectories are implemented on a quadcopter. The flight tests show that by following the designed trajectories, the quadcopter can descend considerably faster than purely vertical trajectories that also avoid the VRS and WBS. [ABSTRACT FROM AUTHOR]