Novel probabilistic and distributed algorithms for guidance, control, and nonlinear estimation of large-scale multi-agent systems

Multi-agent systems are widely used for constructing a desired formation shape, exploring an area, surveillance, coverage, and other cooperative tasks. This dissertation introduces novel algorithms in the three main areas of shape formation, distributed estimation, and attitude control of large-scale multi-agent systems. In the first part of this dissertation, we address the problem of shape formation for thousands to millions of agents. Here, we present two novel algorithms for guiding a large-scale swarm of robotic systems into a desired formation shape in a distributed and scalable manner. These probabilistic swarm guidance algorithms adopt an Eulerian framework, where the physical space is partitioned into bins and the swarm's density distribution over each bin is controlled using tunable Markov chains. In the first algorithm - Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC) - each agent determines its bin transition probabilities using a time-inhomogeneous Markov chain that is constructed in real-time using feedback from the current swarm distribution. This PSG-IMC algorithm minimizes the expected cost of the transitions required to achieve and maintain the desired formation shape, even when agents are added to or removed from the swarm. The algorithm scales well with a large number of agents and complex formation shapes, and can also be adapted for area exploration applications. In the second algorithm - Probabilistic Swarm Guidance using Optimal Transport (PSG-OT) - each agent determines its bin transition probabilities by solving an optimal transport problem, which is recast as a linear program. In the presence of perfect feedback of the current swarm distribution, this algorithm minimizes the given cost function, guarantees faster convergence, reduces the number of transitions for achieving the desired formation, and is robust to disturbances or damages to the formation. We demonstrate the effectiveness of these two proposed swarm guidance algorithms using results from numerical simulations and closed-loop hardware experiments on multiple quadrotors. In the second part of this dissertation, we present two novel discrete-time algorithms for distributed estimation, which track a single target using a network of heterogeneous sensing agents. The Distributed Bayesian Filtering (DBF) algorithm, the sensing agents combine their normalized likelihood functions using the logarithmic opinion pool and the discrete-time dynamic average consensus algorithm. Each agent's estimated likelihood function converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. Using a new proof technique, the convergence, stability, and robustness properties of the DBF algorithm are rigorously characterized. The explicit bounds on the time step of the robust DBF algorithm are shown to depend on the time-scale of the target dynamics. Furthermore, the DBF algorithm for linear-Gaussian models can be cast into a modified form of the Kalman information filter. In the Bayesian Consensus Filtering (BCF) algorithm, the agents combine their estimated posterior pdfs multiple times within each time step using the logarithmic opinion pool scheme. Thus, each agent's consensual pdf minimizes the sum of Kullback-Leibler divergences with the local posterior pdfs. The performance and robust properties of these algorithms are validated using numerical simulations. In the third part of this dissertation, we present an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feed-forward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees global exponential convergence of tracking errors with finite-gain Lp stability in the presence of modeling uncertainties and disturbances, and reduces the resultant disturbance torque. Further, this control law permits the use of any attitude representation and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law, because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional-derivative based reference trajectory, because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control law is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept. The new algorithms proposed in this dissertation will facilitate the development of versatile autonomous multi-agent systems that are capable of performing a variety of complex tasks in a robust and scalable manner

An Innovative Solution to NASA's NEO Impact Threat Mitigation Grand Challenge and Flight Validation Mission Architecture Development

This final technical report describes the results of a NASA Innovative Advanced Concept (NIAC) Phase 2 study entitled "An Innovative Solution to NASA's NEO Impact Threat Mitigation Grand Challenge and Flight Validation Mission Architecture Development." This NIAC Phase 2 study was conducted at the Asteroid Deflection Research Center (ADRC) of Iowa State University in 2012-2014. The study objective was to develop an innovative yet practically implementable solution to the most probable impact threat of an asteroid or comet with short warning time (less than 5 years). The technical materials contained in this final report are based on numerous technical papers, which have been previously published by the project team of the NIAC Phase 1 and 2 studies during the past three years. Those technical papers as well as a NIAC Phase 2 Executive Summary report can be downloaded from the ADRC website (www.adrc.iastate.edu)

High-Fidelity Simulation of Small-Body Lander/Rover Spacecraft

The scientific return of spacecraft missions that explore solar system small bodies can be increased through the inclusion of surface exploration with deployed probes. In this dissertation, a methodology is presented that allows for fast, parallel simulation of bouncing trajectories of arbitrary-shaped ballistic probes in the small-body environment. This enables planning of probe deployment and operation, and supports their inclusion on future missions.The coarse small-body shape is modeled using an implicit signed distance field (SDF) that allows for fast collision detection. Statistical features are included onto the SDF using procedural generation techniques. The small-body gravity field is captured using a voxelization of the classical constant-density polyhedron. Surface interactions between a probe and the surface are accounted for using a hard contact model that takes into account restitution and friction. These models are implemented in a GPU environment to allow for the parallel execution of multiple trajectories.The developed simulation framework is applied to perform parametric investigations of probe deployment, which quantify the effects of relevant properties of a probe and its target small body. The probe shape and internal mass distribution are found to strongly affect its deployment dynamics, with near-spherical probes dispersing over greater regions than more distorted shapes. The effect of the surface interactions coefficients on the different shapes variants is quantified. The presence of statistical surface features is also shown to further influence probe dynamics.Finally, the framework is applied to perform a pre-arrival deployment analysis of the MINERVA-II rovers onboard the Hayabusa-2 spacecraft. This analysis identified challenges in the rover deployment and was used to redesign aspects of the nominal rover release sequence. These models will be used to inform the target site selection and follow-on analysis for the Hayabusa-2 mission rover deployments

Solar-sail mission design for multiple near-Earth asteroid rendezvous

Solar sailing is the use of a thin and lightweight membrane to reflect sunlight and obtain a thrust force on the spacecraft. That is, a sailcraft has a potentially-infinite specific impulse and, therefore, it is an attractive solution to reach mission goals otherwise not achievable, or very expensive in terms of propellant consumption. The recent scientific interest in near-Earth asteroids (NEAs) and the classification of some of those as potentially hazardous asteroids (PHAs) for the Earth stimulated the interest in their exploration. Specifically, a multiple NEA rendezvous mission is attractive for solar-sail technology demonstration as well as for improving our knowledge about NEAs. A preliminary result in a recent study showed the possibility to rendezvous three NEAs in less than ten years. According to the NASA’s NEA database, more than 12,000 asteroids are orbiting around the Earth and more than 1,000 of them are classified as PHA. Therefore, the selection of the candidates for a multiple-rendezvous mission is firstly a combinatorial problem, with more than a trillion of possible combinations with permutations of only three objects. Moreover, for each sequence, an optimal control problem should be solved to find a feasible solar-sail trajectory. This is a mixed combinatorial/optimisation problem, notoriously complex to tackle all at once. Considering the technology constraints of the DLR/ESA Gossamer roadmap, this thesis focuses on developing a methodology for the preliminary design of a mission to visit a number of NEAs through solar sailing. This is divided into three sequential steps. First, two methods to obtain a fast and reliable trajectory model for solar sailing are studied. In particular, a shape-based approach is developed which is specific to solar-sail trajectories. As such, the shape of the trajectory that connects two points in space is designed and the control needed by the sailcraft to follow it is analytically retrieved. The second method exploits the homotopy and continuation theory to find solar-sail trajectories starting from classical low-thrust ones. Subsequently, an algorithm to search through the possible sequences of asteroids is developed. Because of the combinatorial characteristic of the problem and the tree nature of the search space, two criteria are used to reduce the computational effort needed: (a) a reduced database of asteroids is used which contains objects interesting for planetary defence and human spaceflight; and (b) a local pruning is carried out at each branch of the tree search to discard those target asteroids that are less likely to be reached by the sailcraft considered. To reduce further the computational effort needed in this step, the shape-based approach for solar sailing is used to generate preliminary trajectories within the tree search. Lastly, two algorithms are developed which numerically optimise the resulting trajectories with a refined model and ephemerides. These are designed to work with minimum input required by the user. The shape-based approach developed in the first stage is used as an initial-guess solution for the optimisation. This study provides a set of feasible mission scenarios for informing the stakeholders on future mission options. In fact, it is shown that a large number of five-NEA rendezvous missions are feasible in a ten-year launch window, if a solar sail is used. Moreover, this study shows that the mission-related technology readiness level for the available solar-sail technology is larger than it was previously thought and that such a mission can be performed with current or at least near-term solar sail technology. Numerical examples are presented which show the ability of a solar sail both to perform challenging multiple NEA rendezvous and to change the mission en-route

On the dynamics, navigation and control of a spacecraft formation of solar concentrators in the proximity of an asteroid

This purpose of this dissertation is to ascertain whether solar sublimation is a viable method for the deflection of a Near Earth Asteroid. From a research view point, the methods and analysis are applicable to proximal motion around a celestial body, in particular one with a non-Keplerian or irregular orbit as in the case here with the orbit being constantly altered by the deflection action and subject to perturbations, such as solar radiation pressure. Two concepts, and the corresponding dynamics and control, are presented based on previous trade-off and optimisation studies. The first uses a paraboloidic reflector to concentrate the solar radiation onto a solar-pumped laser, which is then directed onto a specific spot on the NEO by a small directional mirror. The spacecraft orbits are designed to fly in formation with the asteroid around the Sun, and are based on the orbital element differences. The formation orbits were optimised based on a number of single and multiple objective functions. A feedback control law is presented for the orbital maintenance required to counteract the solar radiation pressure (due primarily to the large surface area of the primary reflector), and the third-body effects due to the gravitational field of the asteroid. The second option takes advantage of the balance between the gravity attraction of the NEO and solar pressure acting on the collector. The mirror focuses the light directly onto the asteroid surface, controlling the beam by adjusting the focal point of the primary reflector. By altering the shape of the mirror surface, both the focal point and the vector of the solar radiation pressure can be manipulated. An interesting navigation strategy is proposed based on the attitude measurements, the inertial position of each spacecraft, the intersatellite position and velocity measurements, and a 2D image from a rotating onboard camera. The navigational data is used for both the orbital control of the spacecraft and for the beam pointing. The results of simulations of a hypothetical deflection mission of the asteroid Apophis are presented for the dynamics, control, attitude and navigation, accounting for solar radiation pressure, the gravity field of the asteroid, and the deviation of the NEO orbit. The results show that both concepts provide the required deflection with a feasible mass at launch, solving most of the issues related to the solar sublimation method. One of the critical aspects of this deflection concept is properly placing the concentrators in the proximity of the asteroid in order to avoid the plume impingement and the occultation from the asteroid itself. Issues regarding the contamination of the mirrors are addressed and compared with the simulated deflections predicted considering no contamination. Lastly, initial system mass budgets are presented

Discovering sub-micron ice particles across Dione' surface

Water ice is the most abundant component of Saturn’s mid-sized moons. However, these moons show an albedo asymmetry - their leading sides are bright while their trailing side exhibits dark terrains. Such differences arise from two surface alteration processes: (i) the bombardment of charged particles from the interplanetary medium and driven by Saturn’s magnetosphere on the trailing side, and (ii) the impact of E-ring water ice particles on the satellites’ leading side. As a result, the trailing hemisphere appears to be darker than the leading side. This effect is particularly evident on Dione's surface. A consequence of these surface alteration processes is the formation or the implantation of sub-micron sized ice particles.The presence of such particles influences and modifies the surfaces' spectrum because of Rayleigh scattering by the particles. In the near infrared range of the spectrum, the main sub-micron ice grains spectral indicators are: (i) asymmetry and (ii) long ward minimum shift of the absorption band at 2.02 μm (iii) a decrease in the ratio between the band depths at 1.50 and 2.02 μm (iv) a decrease in the height of the spectral peak at 2.6 μm (v) the suppression of the Fresnel reflection peak at 3.1 μm and (vi) the decrease of the reflection peak at 5 μm relative to those at 3.6 μm.We present results from our ongoing work mapping the variation of sub-micron ice grains spectral indicators across Dione' surface using Cassini-VIMS cubes acquired in the IR range (0.8-5.1 μm). To characterize the global variations of spectral indicators across Dione' surface, we divided it into a 1°x1° grid and then averaged the band depths and peak values inside each square cell.We will investigate if there exist a correspondence with water ice abundance variations by producing water ice' absorption band depths at 1.25, 1.52 and 2.02 μm, and with surface morphology by comparing the results with ISS color maps in the ultraviolet, visible and infrared ranges. Finally, we will compare the results with those obtained for Enceladus, Tethys, and Mimas

MAGESTIC: Magnetically Enabled Structures Using Interacting Coils

In our NIAC Phase I study, awarded September 2011, the MIT Space Systems Lab (MIT SSL) began investigating a new structural and mechanical technique aimed at reducing the mass and increasing the stowed-to-deployed ratio of spacecraft systems. This technique uses the magnetic fields from current passing through coils of high temperature superconductors (HTSs) to support spacecraft structures and deploy them to operational configurations from their positions as stowed inside a launch vehicle fairing. These electromagnetic coils are tethered or hinged together in such a way that their motion in some directions or around some axes is constrained, as in Figure 1. Our Phase II study,awarded in Fall 2012, continued this work on electromagnetic structures, with an added focus on developing a new thermal system, investigating additional, non-structural electromagnet functions, and creating a maturation roadmap and plan for addressing barriers to feasibility of the technology. We now call the project MAGESTIC, or Magnetically Enabled STructures using Interacting Coils

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version