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.

This paper considers the problem of stochastic motion planning in uncertain environments, and extends existing chance constrained optimal control solutions. Due to the imperfect knowledge of the system state caused by motion uncertainty, sensor noise and environment uncertainty, the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically. To account for the uncertainty, the constraints are formulated as convex constraints on a random variable, known as chance constraints, with the violation probability of all the constraints guaranteed to be below a threshold. Standard chance constrained stochastic motion planning methods do not incorporate environmental sensing which typically leads to overly-conservative solutions. To address this, a novel hierarchical framework is proposed that consists of two main steps: an expected shortest path problem on an uncertain graph and a chance constrained motion planning problem. The first successful, real-time experimental demonstration of chance constrained control with uncertain constraint parameters and variables is also presented for a quadrotor equipped with a Kinect sensor navigating through an uncertain, cluttered 3D environment.

This paper considers the problem of motion planning for linear, Gaussian systems, and extends existing chance constrained optimal control solutions [1], [2] by incorporating the closed-loop uncertainty of the system and by reducing the conservativeness in the constraints. Due to the imperfect knowledge of the system state caused by motion uncertainty and sensor noise, the constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically. In this work, they are formulated as convex constraints on a univariate Gaussian random variable, with the violation probability of all the constraints guaranteed to be below a threshold. This threshold is a tuning parameter which trades off the performance of the system and the conservativeness of the solution. In contrast to similar methods, the proposed work considers the specific estimator and controller used in the closed-loop system in order to directly characterize the a priori distribution of the closed-loop system state. Using this distribution, a convex optimization program is formulated to solve for the optimal solution for the closed-loop system. The performance of the algorithm is demonstrated through several examples.

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.