Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms

We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure (density) and the forward stochastic reach set. This method is applicable to systems with bounded or unbounded disturbance sets. We also examine the convexity properties of the forward stochastic reach set and its probability density. Motivated by the problem of a robot attempting to capture a stochastically moving, non-adversarial target, we demonstrate our method on two simple examples. Where traditional approaches provide approximations, our method provides exact analytical expressions for the densities and probability of capture.Comment: V3: HSCC 2017 (camera-ready copy), DOI updated, minor changes | V2: Review comments included | V1: 10 pages, 12 figure

A Formal Approach to Verification and Validation of Guidance, Navigation, and Control Algorithms

The traditional Monte Carlo based approaches to Verification & Validation (V&V) of Guidance Navigation and Control (GN&C) algorithms suffers from drawbacks, including typically requiring a significant amount of computational resources to guarantee a candidate algorithm’s appropriateness. Formal approaches to V&V of GN&C algorithms can help address these is-sues as they are not based on simulation. Therefore, we are investigating and developing an innovative formal V&V algorithm for spacecraft GN&C, specifically in the determination of safety of maneuvers for satellite Remote Proximity Operations and Docking (RPOD). Formal V&V methods could provide rigorous and quantifiable assurances of safety for a given satellite maneuver without the need to perform extensive simulations, enhancing the autonomous decision-making capability of a spacecraft with limited computational resources. The research leverages a novel approach to the forward stochastic reachability analysis problem utilizing Fourier transforms. Initial results indicate quantifiable assurance of safety for a maneuvering satellite reach and reach-avoid problem can be achieved that match (sometimes conservatively) the Monte Carlo runs but use up to three or more orders of magnitude less computation resources

Efficiency through Uncertainty: Scalable Formal Synthesis for Stochastic Hybrid Systems

This work targets the development of an efficient abstraction method for formal analysis and control synthesis of discrete-time stochastic hybrid systems (SHS) with linear dynamics. The focus is on temporal logic specifications, both over finite and infinite time horizons. The framework constructs a finite abstraction as a class of uncertain Markov models known as interval Markov decision process (IMDP). Then, a strategy that maximizes the satisfaction probability of the given specification is synthesized over the IMDP and mapped to the underlying SHS. In contrast to existing formal approaches, which are by and large limited to finite-time properties and rely on conservative over-approximations, we show that the exact abstraction error can be computed as a solution of convex optimization problems and can be embedded into the IMDP abstraction. This is later used in the synthesis step over both finite- and infinite-horizon specifications, mitigating the known state-space explosion problem. Our experimental validation of the new approach compared to existing abstraction-based approaches shows: (i) significant (orders of magnitude) reduction of the abstraction error; (ii) marked speed-ups; and (iii) boosted scalability, allowing in particular to verify models with more than 10 continuous variables

Abort-Safe Spacecraft Motion: Reachability Theory and Predictive Control

The increased usage of autonomous systems and vehicles will certainly improve societal transportation and infrastructure in terms of overall performance and safety. For widespread adoption, such systems have to ensure safety under the presence of various faults, conditions and unknown environments. Additionally, vehicle operations need to be robust with respect to potential actuator or path-planning, navigation, and control system failures. This thesis develops an operationally useful and realistic framework for vehicle motion-planning and control algorithms that ensure safe, collision-free trajectories under various actuator failure scenarios. The results are general and applicable to systems with linear time-varying dynamics, but here, the benefits of the approach are shown for various spacecraft relative motion case studies. The methodology makes use of backwards reachable sets, which are used to characterize the unsafe region of state space from which, in the presence of a failure, a collision between a chaser and a target vehicle cannot be avoided. That is, in this region of state space no feasible evasive collision-avoidance maneuvers exist. Additionally, the passively unsafe state space or the sets of states that result in free-drift collisions with the target, due to total loss of control actuation, are characterized. A chaser spacecraft is guided towards a target body via a model predictive control trajectory generation scheme that ensures abort-safety by avoiding the a-priori computed unsafe region of state space. To ensure problem tractability in real-time, the original non-convex motion-planning problem is convexified online using local half-space that separate the chaser spacecraft from the unsafe region of state space. This ensures that the chaser approaches its target in an inherently abort-safe manner. Simulations of the rendezvous planning and control policy on various orbits demonstrate how the approach ensures passive and active aborts that are safe in the event of various thruster failures. Finally, the developed work used to characterize the regions of state space that are passively unsafe, are described using orbital elements differences, which has a few benefits. Such sets have reduced linearization errors ensuring higher accuracy when characterizing the passively unsafe regions of state space compared with the same sets expressed using Cartesian coordinates. As such, the linear domain in which the safety analysis is performed is enlarged. Naturally, these sets are mostly useful for formation flying scenarios where the controlled vehicle is close to the target region. However, we provide insights as to how such sets can be used for the purposes of both safe formation and constellation design.</p

ROS Based High Performance Control Architecture for an Aerial Robotic Testbed

The purpose of this thesis is to show the development of an aerial testbed based on the Robot Operating System (ROS). Such a testbed provides flexibility to control heterogenous vehicles, since the robots are able to simply communication with each other on the High Level (HL) control side. ROS runs on an embedded computer on-board each quadrotor. This eliminates the need of a Ground Base Station, since the complete HL control runs on-board the Unmanned Aerial Vehicle (UAV). The architecture of the system is explained throughout the thesis with detailed explanations of the specific hardware and software used for the system. The implementation on two different quadrotor models is documented and shows that even though they have different components, they can be controlled similarly by the framework. The user is able to control every unit of the testbed with position, velocity and/or acceleration data. To show this independency, control architectures are shown and implemented. Extensive tests verify their effectiveness. The flexibility of the proposed aerial testbed is demonstrated by implementing several applications that require high-performance control. Additionally, a framework for a flying inverted pendulum on a quadrotor using robust hybrid control is presented. The goal is to have a universal controller which is able to swing-up and balance an off-centered pendulum that is attached to the UAV linearly and rotationally. The complete dynamic model is derived and a control strategy is presented. The performance of the controller is demonstrated using realistic simulation studies. The realization in the testbed is documented with modifications that were made to the quadrotor to attach the pendulum. First flight tests are conducted and are presented. The possibilities of using a ROS based framework is shown at every step. It has many advantages for implementation purposes, especially in a heterogeneous robotic environment with many agents. Real-time data of the robot is provided by ROS topics and can be used at any point in the system. The control architecture has been validated and verified with different practical tests, which also allowed improving the system by tuning the specific control parameters