Proving that systems satisfy hard input and state constraints is frequently desirable when designing cyber-physical systems. One method for doing so is to compute the viability kernel, the subset of the state space for which a control signal exists that is guaranteed to keep the system within the constraints over some time horizon. In this paper we present a novel method for approximating the viability kernel for linear sampled-data systems using a sampling-based algorithm, which by its construction offers a direct trade-off between scalability and accuracy. We also prove that the algorithm is correct, that its convergence properties are optimal, and demonstrate it on a simple example. We conclude by briefly describing additional results which are omitted due to space constraints.

This talk will present reachability analysis as a tool for model checking and controller synthesis for dynamic systems. We will consider the problem of guaranteeing reachability to a given desired subset of the state space while satisfying a safety property defined in terms of state constraints. We allow for nonlinear and hybrid dynamics, and possibly nonconvex state constraints. We use these results to synthesize controllers that ensure safety and reachability properties under bounded model disturbances that vary continuously.

While machine learning techniques have become popular tools in the design of autonomous systems, the asymptotic nature of their performance guarantees means that they should not be used in scenarios in which safety and robustness are critical for success. By pairing machine learning algorithms with rigorous safety analyses, such as Hamilton-Jacobi-Isaacs (HJI) reachability, this limitation can be overcome. Guaranteed Safe Online Learning via Reachability (GSOLR) is a framework which combines HJI reachability with general machine learning techniques, allowing for the design of robotic systems which demonstrate both high performance and guaranteed safety. In this paper we show how the GSOLR framework can be applied to a target tracking problem, in which an observing quadrotor helicopter must keep a target ground vehicle with unknown (but bounded) dynamics inside its field of view at all times, while simultaneously attempting to build a motion model of the target. The resulting algorithm was implemented on board the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control, and was compared to a naive safety-only algorithm and a learning-only algorithm. Experimental results illustrate the success of the GSOLR algorithm, even under scenarios in which the machine learning algorithm performed poorly (and would otherwise lead to unsafe actions), thus demonstrating the power of this technique.

For some time now machine learning methods have been widely used in perception for autonomous robots. While there have been many results describing the performance of machine learning techniques with regards to their accuracy or convergence rates, relatively little work has been done on developing theoretical performance guarantees about their stability and robustness. As a result, many machine learning techniques are still limited to being used in situations where safety and robustness are not critical for success. One way to overcome this difficulty is by using reachability analysis, which can be used to compute regions of the state space, known as reachable sets, from which the system can be guaranteed to remain safe over some time horizon regardless of the disturbances. In this paper we show how reachability analysis can be combined with machine learning in a scenario in which an aerial robot is attempting to learn the dynamics of a ground vehicle using a camera with a limited field of view. The resulting simulation data shows that by combining these two paradigms, one can create robotic systems that feature the best qualities of each, namely high performance and guaranteed safety.

For many applications, the control of a complex nonlinear system can be made easier by modeling the system as a collection of simplified hybrid modes, each representing a particular operating regime. An example of this is the decomposition of complex aerobatic flights into sequences of discrete maneuvers, an approach that has proven very successful for both human piloted and autonomously controlled aircraft. However, a critical step when designing such control systems is to ensure the safety and feasibility of transitions between these maneuvers. This work presents a hybrid dynamics framework for the design of guaranteed safe switching regions and is applied to a quadrotor helicopter performing an autonomous backflip. The regions are constructed using reachable sets calculated via a Hamilton-Jacobi differential game formulation, and experimental results are presented from flight tests on the STARMAC quadrotor platform.

The Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control, a fleet of quadrotor helicopters, has been developed as a testbed for novel algorithms that enable autonomous operation of aerial vehicles. The testbed has been used to validate multiple algorithms such as reactive collision avoidance, collision avoidance through Nash Bargaining, path planning, cooperative search and aggressive maneuvering. This article briefly describes the algorithms presented and provides references for a more in-depth formulation, and the accompanying movie shows the demonstration of the algorithms on the testbed.