Safe Onboard Guidance and Control Under Probabilistic Uncertainty

An algorithm was developed that determines the fuel-optimal spacecraft guidance trajectory that takes into account uncertainty, in order to guarantee that mission safety constraints are satisfied with the required probability. The algorithm uses convex optimization to solve for the optimal trajectory. Convex optimization is amenable to onboard solution due to its excellent convergence properties. The algorithm is novel because, unlike prior approaches, it does not require time-consuming evaluation of multivariate probability densities. Instead, it uses a new mathematical bounding approach to ensure that probability constraints are satisfied, and it is shown that the resulting optimization is convex. Empirical results show that the approach is many orders of magnitude less conservative than existing set conversion techniques, for a small penalty in computation time

Minimum Landing Error Powered-Descent Guidance for Planetary Missions

An algorithm improves the accuracy with which a lander can be delivered to the surface of Mars. The main idea behind this innovation is the use of a lossless convexification, which converts an otherwise non-convex constraint related to thruster throttling to a convex constraint, enabling convex optimization to be used. The convexification leads directly to an algorithm that guarantees finding the global optimum of the original nonconvex optimization problem with a deterministic upper bound on the number of iterations required for convergence. In this innovation, previous work in powered-descent guidance using convex optimization is extended to handle the case where the lander must get as close as possible to the target given the available fuel, but is not required to arrive exactly at the target. The new algorithm calculates the minimum-fuel trajectory to the target, if one exists, and calculates the trajectory that minimizes the distance to the target if no solution to the target exists. This approach poses the problem as two Second-Order Cone Programs, which can be solved to global optimality with deterministic bounds on the number of iterations required

A Combined Stochastic and Greedy Hybrid Estimation Capability for Concurrent Hybrid Models with Autonomous Mode Transitions

Robotic and embedded systems have become increasingly pervasive in applicationsranging from space probes and life support systems to robot assistants. In order to act robustly in the physical world, robotic systems must be able to detect changes in operational mode, such as faults, whose symptoms manifest themselves only in the continuous state. In such systems, the state is observed indirectly, and must therefore be estimated in a robust, memory-efficient manner from noisy observations.Probabilistic hybrid discrete/continuous models, such as Concurrent Probabilistic Hybrid Automata (CPHA) are convenient modeling tools for such systems. In CPHA, the hidden state is represented with discrete and continuous state variables that evolve probabilistically. In this paper, we present a novel method for estimating the hybrid state of CPHA that achieves robustness by balancing greedy and stochastic search. The key insight is that stochastic and greedy search methods, taken together, are often particularly effective in practice.To accomplish this, we first develop an efficient stochastic sampling approach for CPHA based on Rao-Blackwellised Particle Filtering. We then propose a strategy for mixing stochastic and greedy search. The resulting method is able to handle three particularly challenging aspects of real-world systems, namely that they 1) exhibit autonomous mode transitions, 2) consist of a large collection of concurrently operating components, and 3) are non-linear. Autonomous mode transitions, that is, discrete transitions that depend on thecontinuous state, are particularly challenging to address, since they couple the discrete and continuous state evolution tightly. In this paper we extend the class of autonomous mode transitions that can be handled to arbitrary piecewise polynomial transition distributions.We perform an empirical comparison of the greedy and stochastic approaches to hybrid estimation, and then demonstrate the robustness of the mixed method incorporated with our HME (Hybrid Mode Estimation) capability. We show that this robustness comes at only a small performance penalty

Chance-Constrained Optimal Path Planning With Obstacles

Autonomous vehicles need to plan trajectories to a specified goal that avoid obstacles. For robust execution, we must take into account uncertainty, which arises due to uncertain localization, modeling errors, and disturbances. Prior work handled the case of set-bounded uncertainty. We present here a chance-constrained approach, which uses instead a probabilistic representation of uncertainty. The new approach plans the future probabilistic distribution of the vehicle state so that the probability of failure is below a specified threshold. Failure occurs when the vehicle collides with an obstacle or leaves an operator-specified region. The key idea behind the approach is to use bounds on the probability of collision to show that, for linear-Gaussian systems, we can approximate the nonconvex chance-constrained optimization problem as a disjunctive convex program. This can be solved to global optimality using branch-and-bound techniques. In order to improve computation time, we introduce a customized solution method that returns almost-optimal solutions along with a hard bound on the level of suboptimality. We present an empirical validation with an aircraft obstacle avoidance example.National Science Foundation (U.S.) (Grant IIS-1017992)Boeing Company (Grant MIT-BA-GTA-1

Cooperative Control with Adaptive Graph Laplacians for Spacecraft Formation Flying

This paper investigates exact nonlinear dynamics and cooperative control for spacecraft formation flying with Earth oblateness (J2 perturbation) and atmospheric drag effects. The nonlinear dynamics for chief and deputy motions are derived by using Gauss' variational equation and the Euler-Lagrangian formulation, respectively. The proposed cooperative control employs adaptive time-varying Laplacian gains. The tracking and diffusive coupling gains are adapted by the synchronization/tracking errors and distance-based connectivity, thereby defining a time-varying network topology. Moreover, the proposed method relaxes the network structure requirement and permits an unbalanced graph. Nonlinear stability is proven by contraction analysis and incremental input-to-state stability. Numerical examples show the effectiveness of the proposed method

Spacecraft Guidance, Navigation, and Control Visualization Tool

G-View is a 3D visualization tool for supporting spacecraft guidance, navigation, and control (GN&C) simulations relevant to small-body exploration and sampling (see figure). The tool is developed in MATLAB using Virtual Reality Toolbox and provides users with the ability to visualize the behavior of their simulations, regardless of which programming language (or machine) is used to generate simulation results. The only requirement is that multi-body simulation data is generated and placed in the proper format before applying G-View

Adaptation of G-TAG Software for Validating Touch-and-Go Comet Surface Sampling Design Methodology

The G-TAG software tool was developed under the R&TD on Integrated Autonomous Guidance, Navigation, and Control for Comet Sample Return, and represents a novel, multi-body dynamics simulation software tool for studying TAG sampling. The G-TAG multi-body simulation tool provides a simulation environment in which a Touch-and-Go (TAG) sampling event can be extensively tested. TAG sampling requires the spacecraft to descend to the surface, contact the surface with a sampling collection device, and then to ascend to a safe altitude. The TAG event lasts only a few seconds but is mission-critical with potentially high risk. Consequently, there is a need for the TAG event to be well characterized and studied by simulation and analysis in order for the proposal teams to converge on a reliable spacecraft design. This adaptation of the G-TAG tool was developed to support the Comet Odyssey proposal effort, and is specifically focused to address comet sample return missions. In this application, the spacecraft descends to and samples from the surface of a comet. Performance of the spacecraft during TAG is assessed based on survivability and sample collection performance. For the adaptation of the G-TAG simulation tool to comet scenarios, models are developed that accurately describe the properties of the spacecraft, approach trajectories, and descent velocities, as well as the models of the external forces and torques acting on the spacecraft. The adapted models of the spacecraft, descent profiles, and external sampling forces/torques were more sophisticated and customized for comets than those available in the basic G-TAG simulation tool. Scenarios implemented include the study of variations in requirements, spacecraft design (size, locations, etc. of the spacecraft components), and the environment (surface properties, slope, disturbances, etc.). The simulations, along with their visual representations using G-View, contributed to the Comet Odyssey New Frontiers proposal effort by indicating problems and/or benefits of different approaches and designs

Graph-Based Path-Planning for Titan Balloons

A document describes a graph-based path-planning algorithm for balloons with vertical control authority and little or no horizontal control authority. The balloons are designed to explore celestial bodies with atmospheres, such as Titan, a moon of Saturn. The algorithm discussed enables the balloon to achieve horizontal motion using the local horizontal winds. The approach is novel because it enables the balloons to use arbitrary wind field models. This is in contrast to prior approaches that used highly simplified wind field models, such as linear, or binary, winds. This new approach works by discretizing the space in which the balloon operates, and representing the possible states of the balloon as a graph whose arcs represent the time taken to move from one node to another. The approach works with arbitrary wind fields, by looking up the wind strength and direction at every node in the graph from an arbitrary wind model. Having generated the graph, search techniques such as Dijkstra s algorithm are then used to find the set of vertical actuation commands that takes the balloon from the start to the goal in minimum time. In addition, the set of reachable locations on the moon or planet can be determined

Powered Descent Guidance with General Thrust-Pointing Constraints

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints

Robust execution for stochastic hybrid systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 177-180).Unmanned systems, such as Autonomous Underwater Vehicles (AUVs), planetary rovers and space probes, have enormous potential in areas such as reconnaissance and space exploration. However the effectiveness and robustness of these systems is currently restricted by a lack of autonomy. Previous work introduced the concept of a model-based executive, which increases the level of autonomy, elevating the level at which systems are commanded. This simplifies the operator's task and leaves degrees of freedom in the plan that allow the executive to optimize resources and ensure robustness to uncertainty. Uncertainty arises due to uncertain state estimation, disturbances, model uncertainty and component failures. This thesis develops a model-based executive that reasons explicitly from a stochastic hybrid discrete-continuous system model to find the optimal course of action, while ensuring the required level of robustness to uncertainty is achieved. Our first contribution is a novel 'Particle Control' approach for robust execution of state plans with stochastic hybrid systems. We introduce the notion of chance-constrained state plan execution; this means that the executive ensures tasks in the state plan have at least a specified minimum probability of success. The minimum probabilities are specified by the operator, enabling conservatism to be traded against performance. In order to make optimal chance-constrained execution tractable, the Particle Control approach approximates the system's state distribution using samples or 'particles' and optimizes the evolution of these particles to achieve chance-constrained state plan execution. In this manner particle control solves a tractable deterministic approximation to the original stochastic problem; furthermore the approximation becomes exact as the number of particles approaches infinity.(cont.) For an important class of hybrid discrete-continuous system known as Jump Markov Linear Systems, the resulting deterministic optimization can be posed as a Mixed Integer Linear Program and solved to global optimality using efficient commercially-available solvers. Our second contribution is 'active' hybrid estimation subject to state plan constraints. Exact hybrid state estimation in stochastic hybrid systems is, in general, intractable. Tractable approximate hybrid estimation methods can lose track of the true hybrid state. In this thesis we develop an active hybrid estimation capability, which probes the system in order to reduce uncertainty in the hybrid state. This approach generates control sequences to minimize the probability of approximate hybrid estimation losing the true mode sequence, while ensuring that the state plan is satisfied subject to chance constraints. In order to make this problem tractable, we develop an analytic upper bound on the probability of losing the true mode sequence, and use a convex constraint tightening approach to approximate the chance constraints in the problem. Our final contribution is a novel hybrid model-learning approach. Specifying accurate hybrid system models is essential for accurate estimation and control, but is also extremely challenging. The hybrid executive must therefore determine hybrid system models from observed data. In this thesis we present an approximate Expectation-Maximization method for hybrid model learning; this method extends prior approaches to deal with mode transitions that depend on the continuous state.by Lars James Christopher Blackmore.Ph.D