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This letter considers assignment problems consisting of n pursuers attempting to intercept n targets. We consider stationary targets as well as targets maneuvering toward an asset. The assignment algorithm relies on an n x n cost matrix where entry (i, j) is the minimum time for pursuer i to intercept target j. Each entry of this matrix requires the solution of a nonlinear optimal control problem. This subproblem is computationally intensive and hence the computational cost of the assignment is dominated by the construction of the cost matrix. We propose to use neural networks for function approximation of the minimum time until intercept. The neural networks are trained offline, thus allowing for real-time online construction of cost matrices. Moreover, the function approximators have sufficient accuracy to obtain reasonable solutions to the assignment problem. In most cases, the approximators achieve assignments with optimal worst case intercept time. The proposed approach is demonstrated on several examples with increasing numbers of pursuers and targets., Comment: 6 pages, 6 tables, 1 figure. Presented at the 2022 American Control Conference

Leveraging advancements in micro-scale technology, we propose a fleet of autonomous, low-cost, small solar sails for interplanetary exploration. The Berkeley Low-cost Interplanetary Solar Sail (BLISS) project aims to utilize small-scale technologies to create a fleet of tiny interplanetary femto-spacecraft for rapid, low-cost exploration of the inner solar system. This paper describes the hardware required to build a nearly 10 g spacecraft using a 1 m$^2$ solar sail steered by micro-electromechanical systems (MEMS) inchworm actuators. The trajectory control to a NEO, here 101955 Bennu, is detailed along with the low-level actuation control of the solar sail and the specifications of proposed onboard communication and computation. Two other applications are also shortly considered: sample return from dozens of Jupiter-family comets and interstellar comet rendezvous and imaging. The paper concludes by discussing the fundamental scaling limits and future directions for steerable autonomous miniature solar sails with onboard custom computers and sensors., Comment: 16 pages, 13 figures, 5 tables, 23 equations, and just over 10 years

Large (> 1000kg), expensive (> $1bn), monolithic, flagship-class satellites (e.g., Hubble, Chandra, James Webb telescopes) may soon be overshadowed by constellations of many, smaller, cheaper, more agile spacecraft working together as a coordinated system. In this work, we study several important attitude and orbit control problems relevant to the formation and operation of small spacecraft constellations. Our example problems include agile attitude maneuvering for multi-target acquisition in an Earth observation application, a centralized approach to constellation formation in low Earth orbit, a distributed approach to constellation formation in Mars areostationary orbit, and orbital rendezvous with objects in the inner Solar System. Our main tool is trajectory optimization, an approach that is appropriate for spacecraft applications where we often seek solutions that are optimal (e.g., minimum-time, minimum-fuel, minimum-control-effort) in the presence of mission or spacecraft constraints. We employ recent advances in sequential convex programming to efficiently handle the nonlinear dynamics and non-convex constraints that exist in our problem formulations.

Large (> 1000kg), expensive (> $1bn), monolithic, flagship-class satellites (e.g., Hubble, Chandra, James Webb telescopes) may soon be overshadowed by constellations of many, smaller, cheaper, more agile spacecraft working together as a coordinated system. In this work, we study several important attitude and orbit control problems relevant to the formation and operation of small spacecraft constellations. Our example problems include agile attitude maneuvering for multi-target acquisition in an Earth observation application, a centralized approach to constellation formation in low Earth orbit, a distributed approach to constellation formation in Mars areostationary orbit, and orbital rendezvous with objects in the inner Solar System. Our main tool is trajectory optimization, an approach that is appropriate for spacecraft applications where we often seek solutions that are optimal (e.g., minimum-time, minimum-fuel, minimum-control-effort) in the presence of mission or spacecraft constraints. We employ recent advances in sequential convex programming to efficiently handle the nonlinear dynamics and non-convex constraints that exist in our problem formulations.

Agile attitude maneuvering maximizes the utility of remote sensing satellite constellations. By taking into account a satellite's physical properties and its actuator specifications, we may leverage the full performance potential of the attitude control system to conduct agile remote sensing beyond conventional slew-and-stabilize maneuvers. Employing a constellation of agile satellites, coordinated by an autonomous and responsive scheduler, can significantly increase overall response rate, revisit time and global coverage for the mission. In this paper, we use recent advances in sequential convex programming based trajectory optimization to enable rapid-target acquisition, pointing and tracking capabilities for a scheduler-based constellation. We present two problem formulations. The Minimum-Time Slew Optimal Control Problem determines the minimum time, required energy, and optimal trajectory to slew between any two orientations given nonlinear quaternion kinematics, gyrostat and actuator dynamics, and state/input constraints. By gridding the space of 3D rotations and efficiently solving this problem on the grid, we produce lookup tables or parametric fits off-line that can then be used on-line by a scheduler to compute accurate estimates of minimum-time and maneuver energy for real-time constellation scheduling. The Minimum-Effort Multi-Target Pointing Optimal Control Problem is used on-line by each satellite to produce continuous attitude-state and control-input trajectories that realize a given schedule while minimizing attitude error and control effort. The optimal trajectory may then be achieved by a low-level tracking controller. We demonstrate our approach with an example of a reference satellite in Sun-synchronous orbit passing over globally-distributed, Earth-observation targets., Comment: 24 pages, 27 figures

We study a multi-body asset-guarding game in missile defense where teams of interceptor missiles collaborate to defend a non-manuevering asset against a group of threat missiles. We approach the problem in two steps. We first formulate an assignment problem where we optimally assign subsets of collaborating interceptors to each threat so that all threats are intercepted as far away from the asset as possible. We assume that each interceptor is controlled by a collaborative guidance law derived from linear quadratic dynamic games. Our results include a 6-DOF simulation of a 5-interceptor versus 3-threat missile engagement where each agent is modeled as a missile airframe controlled by an autopilot. Despite the assumption of linear dynamics in our collaborative guidance law and the unmodeled dynamics in the simulation environment (e.g., varying density and gravity), we show that the simulated trajectories match well with those predicted by our approach. Furthermore, we show that a more agile threat, with greater speed and acceleration, can be intercepted by inferior interceptors when they collaborate. We believe the concepts introduced in this paper may be applied in asymmetric missile defense scenarios, including defense against advanced cruise missiles and hypersonic vehicles.

We present a distributed control law to assemble a cluster of satellites into an equally-spaced, planar constellation in a desired circular orbit about a planet. We assume each satellite only uses local information, transmitted through communication links with neighboring satellites. The same control law is used to maintain relative angular positions in the presence of disturbance forces. The stability of the constellation in the desired orbit is proved using a compositional approach. We first show the existence and uniqueness of an equilibrium of the interconnected system. We then certify each satellite and communication link is equilibrium-independent passive with respective storage functions. By leveraging the skew symmetric coupling structure of the constellation and the equilibrium-independent passivity property of each subsystem, we show that the equilibrium of the interconnected system is stable with a Lyapunov function composed of the individual subsystem storage functions. We further prove that the angular velocity of each satellite converges to the desired value necessary to maintain circular, areostationary orbit. Finally, we present simulation results to demonstrate the efficacy of the proposed control law in acquisition and station-keeping of an equally-spaced satellite constellation in areostationary orbit despite the presence of unmodeled disturbance forces.

We present a numerical approach to finding optimal trajectories for players in a multi-body, asset-guarding game with nonlinear dynamics and non-convex constraints. Using the Iterative Best Response (IBR) scheme, we solve for each player's optimal strategy assuming the other players' trajectories are known and fixed. Leveraging recent advances in Sequential Convex Programming (SCP), we use SCP as a subroutine within the IBR algorithm to efficiently solve an approximation of each player's constrained trajectory optimization problem. We apply the approach to an asset-guarding game example involving multiple pursuers and a single evader (i.e., n-versus-1 engagements). Resulting evader trajectories are tested in simulation to verify successful evasion against pursuers using conventional intercept guidance laws.

We study the optimal control of an arbitrarily large constellation of small satellites operating in low Earth orbit. Simulating the lack of on-board propulsion, we limit our actuation to the use of differential drag maneuvers to make in-plane changes to the satellite orbits. We propose an efficient method to separate a cluster of satellites into a desired constellation shape while respecting actuation constraints and maximizing the operational lifetime of the constellation. By posing the problem as a linear program, we solve for the optimal drag commands for each of the satellites on a daily basis with a shrinking-horizon model predictive control approach. We then apply this control strategy in a nonlinear orbital dynamics simulation with a simple, varying atmospheric density model. We demonstrate the ability to control a cluster of 100+ satellites starting at the same initial conditions in a circular low Earth orbit to form an equally spaced constellation (with a relative angular separation error tolerance of one-tenth a degree). The constellation separation task can be executed in 71 days, a time frame that is competitive for the state-of-the-practice. This method allows us to trade the time required to converge to the desired constellation with a sacrifice in the overall constellation lifetime, measured as the maximum altitude loss experienced by one of the satellites in the group after the separation maneuvers., Comment: 8 pages, 9 figures

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007., Includes bibliographical references (leaf 38)., With energy and environmental concerns becoming increasingly greater issues, electric vehicles are a promising alternative to internal combustion engine vehicles. More research and interest must be focused on battery technology and electric vehicles to make this a viable solution for the future of transportation. This project focuses on converting a 1974 Porsche 914, originally equipped with a 4-cylinder IC engine, into a full electric vehicle. The IC engine is replaced with a 50kW peak, 3-phase AC induction motor powered by twelve lithium-ion phosphate-metal cathode batteries. This paper goes through the conversion process as well as the necessary maintenance and driving techniques required to safely and efficiently operate an electric vehicle. Although the vehicle is complete it is currently in the debugging phase due to unforeseen electrical problems. The vehicle is planned to run by early June, 2007. Despite this setback, the project has been successful in starting a performance electric vehicle team, MIT EVT, and in increasing the appeal of electric vehicles in the MIT community., by Emmanuel J. Sin., S.B.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007., Includes bibliographical references (leaf 38)., With energy and environmental concerns becoming increasingly greater issues, electric vehicles are a promising alternative to internal combustion engine vehicles. More research and interest must be focused on battery technology and electric vehicles to make this a viable solution for the future of transportation. This project focuses on converting a 1974 Porsche 914, originally equipped with a 4-cylinder IC engine, into a full electric vehicle. The IC engine is replaced with a 50kW peak, 3-phase AC induction motor powered by twelve lithium-ion phosphate-metal cathode batteries. This paper goes through the conversion process as well as the necessary maintenance and driving techniques required to safely and efficiently operate an electric vehicle. Although the vehicle is complete it is currently in the debugging phase due to unforeseen electrical problems. The vehicle is planned to run by early June, 2007. Despite this setback, the project has been successful in starting a performance electric vehicle team, MIT EVT, and in increasing the appeal of electric vehicles in the MIT community., by Emmanuel J. Sin., S.B.