Safe Coverage of Compact Domains For Second Order Dynamical Systems

Autonomous systems operating in close proximity with each other to cover a specified area has many potential applications, but to achieve effective coordination, two key challenges need to be addressed: coordination and safety. For coordination, we propose a locally asymptotically stable distributed coverage controller for compact domains in the plane and homogeneous vehicles modeled with second order dynamics with bounded input forces. This control policy is based on artificial potentials designed to enforce desired vehicle-domain and inter-vehicle separations, and can be applied to arbitrary compact domains including non-convex ones. We prove, using Lyapunov theory, that certain coverage configurations are locally asymptotically stable. For safety, we utilize Hamilton-Jacobi (HJ) reachability theory to guarantee pairwise collision avoidance. Rather than computing numerical solutions of the associated HJ partial differential equation as is typically done, we derive an analytical solution for our second-order vehicle model. This provides an exact, global solution rather than an approximate, local one within some computational domain. In addition to considerably reducing collision count, the collision avoidance controller also reduces oscillatory behaviour of vehicles, helping the system reach steady state faster. We demonstrate our approach in three representative simulations involving a square domain, triangle domain, and a non-convex moving domain.Comment: 8 pages, 6 figures, IFAC 2020 initial submissio

Automated Synthesis of Safe Digital Controllers for Sampled-Data Stochastic Nonlinear Systems

We present a new method for the automated synthesis of digital controllers with formal safety guarantees for systems with nonlinear dynamics, noisy output measurements, and stochastic disturbances. Our method derives digital controllers such that the corresponding closed-loop system, modeled as a sampled-data stochastic control system, satisfies a safety specification with probability above a given threshold. The proposed synthesis method alternates between two steps: generation of a candidate controller pc, and verification of the candidate. pc is found by maximizing a Monte Carlo estimate of the safety probability, and by using a non-validated ODE solver for simulating the system. Such a candidate is therefore sub-optimal but can be generated very rapidly. To rule out unstable candidate controllers, we prove and utilize Lyapunov's indirect method for instability of sampled-data nonlinear systems. In the subsequent verification step, we use a validated solver based on SMT (Satisfiability Modulo Theories) to compute a numerically and statistically valid confidence interval for the safety probability of pc. If the probability so obtained is not above the threshold, we expand the search space for candidates by increasing the controller degree. We evaluate our technique on three case studies: an artificial pancreas model, a powertrain control model, and a quadruple-tank process.Comment: 12 pages, 4 figures, 4 table

Comparison between safety methods control barrier function vs. reachability analysis

This report aims to compare two safety methods: control barrier function and Hamilton-Jacobi reachability analysis. We will consider the difference with a focus on the following aspects: generality of system dynamics, difficulty of construction and computation cost. A standard Dubins car model will be evaluated numerically to make the comparison more concrete

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019

Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties

Robots operating in real world settings must navigate and maintain safety while interacting with many heterogeneous agents and obstacles. Multi-Agent Control Barrier Functions (CBF) have emerged as a computationally efficient tool to guarantee safety in multi-agent environments, but they assume perfect knowledge of both the robot dynamics and other agents' dynamics. While knowledge of the robot's dynamics might be reasonably well known, the heterogeneity of agents in real-world environments means there will always be considerable uncertainty in our prediction of other agents' dynamics. This work aims to learn high-confidence bounds for these dynamic uncertainties using Matrix-Variate Gaussian Process models, and incorporates them into a robust multi-agent CBF framework. We transform the resulting min-max robust CBF into a quadratic program, which can be efficiently solved in real time. We verify via simulation results that the nominal multi-agent CBF is often violated during agent interactions, whereas our robust formulation maintains safety with a much higher probability and adapts to learned uncertainties

Safe Learning of Quadrotor Dynamics Using Barrier Certificates

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.Comment: Submitted to ICRA 2018, 8 page

Reactive Integrated Mission and Motion planning

Correct-by-construction manipulation planning in a dynamic environment, where other agents can manipulate objects in the workspace, is a challenging problem. The tight coupling of actions and motions between agents and complexity of mission specifications makes the problem computationally intractable. This paper presents a reactive integrated mission and motion planning for mobile-robot manipulator systems operating in a partially known environment. We introduce a multi-layered synergistic framework that receives high-level mission specifications expressed in linear temporal logic and generates dynamically-feasible and collision-free motion trajectories to achieve it. In the high-level layer, a mission planner constructs a symbolic two-player game between the robots and their environment to synthesis a strategy that adapts to changes in the workspace imposed by other robots. A bilateral synergistic layer is developed to map the designed mission plan to an integrated task and motion planner, constructing a set of robot tasks to move the objects according to the mission strategy. In the low-level planning stage, verifiable motion controllers are designed that can be incrementally composed to guarantee a safe motion planning for each high-level induced task. The proposed framework is illustrated with a multi-robot warehouse example with the mission of moving objects to various locations.Comment: ACC 2018 Conferenc

Modelling and analyzing adaptive self-assembling strategies with Maude

Building adaptive systems with predictable emergent behavior is a challenging task and it is becoming a critical need. The research community has accepted the challenge by introducing approaches of various nature: from software architectures, to programming paradigms, to analysis techniques. We recently proposed a conceptual framework for adaptation centered around the role of control data. In this paper we show that it can be naturally realized in a reflective logical language like Maude by using the Reflective Russian Dolls model. Moreover, we exploit this model to specify, validate and analyse a prominent example of adaptive system: robot swarms equipped with self-assembly strategies. The analysis exploits the statistical model checker PVeStA

Separation of distributed coordination and control for programming reliable robotics

A robot's code needs to sense the environment, control the hardware, and communicate with other robots. Current programming languages do not provide the necessary hardware platform-independent abstractions, and therefore, developing robot applications require detailed knowledge of signal processing, control, path planning, network protocols, and various platform-specific details. Further, porting applications across hardware platforms becomes tedious. With the aim of separating these hardware dependent and independent concerns, we have developed Koord: a domain specific language for distributed robotics. Koord abstracts platform-specific functions for sensing, communication, and low-level control. Koord makes the platform-independent control and coordination code portable and modularly verifiable. It raises the level of abstraction in programming by providing distributed shared memory for coordination and port interfaces for sensing and control. We have developed the formal executable semantics of Koord in the K framework. With this symbolic execution engine, we can identify proof obligations for gaining high assurance from Koord applications. Koord is deployed on CyPhyHouse---a toolchain that aims to provide programming, debugging, and deployment benefits for distributed mobile robotic applications. The modular, platform-independent middleware of CyPhyHouse implements these functionalities using standard algorithms for path planning (RRT), control (MPC), mutual exclusion, etc. A high-fidelity, scalable, multi-threaded simulator for Koord applications is developed to simulate the same application code for dozens of heterogeneous agents. The same compiled code can also be deployed on heterogeneous mobile platforms. This thesis outlines the design, implementation and formalization of the Koord language and the main components of CyPhyHouse that it is deployed on

Towards Provably Not-at-Fault Control of Autonomous Robots in Arbitrary Dynamic Environments

As autonomous robots increasingly become part of daily life, they will often encounter dynamic environments while only having limited information about their surroundings. Unfortunately, due to the possible presence of malicious dynamic actors, it is infeasible to develop an algorithm that can guarantee collision-free operation. Instead, one can attempt to design a control technique that guarantees the robot is not-at-fault in any collision. In the literature, making such guarantees in real time has been restricted to static environments or specific dynamic models. To ensure not-at-fault behavior, a robot must first correctly sense and predict the world around it within some sufficiently large sensor horizon (the prediction problem), then correctly control relative to the predictions (the control problem). This paper addresses the control problem by proposing Reachability-based Trajectory Design for Dynamic environments (RTD-D), which guarantees that a robot with an arbitrary nonlinear dynamic model correctly responds to predictions in arbitrary dynamic environments. RTD-D first computes a Forward Reachable Set (FRS) offline of the robot tracking parameterized desired trajectories that include fail-safe maneuvers. Then, for online receding-horizon planning, the method provides a way to discretize predictions of an arbitrary dynamic environment to enable real-time collision checking. The FRS is used to map these discretized predictions to trajectories that the robot can track while provably not-at-fault. One such trajectory is chosen at each iteration, or the robot executes the fail-safe maneuver from its previous trajectory which is guaranteed to be not at fault. RTD-D is shown to produce not-at-fault behavior over thousands of simulations and several real-world hardware demonstrations on two robots: a Segway, and a small electric vehicle.Comment: 10 pages, 3 figure