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.

We present an efficient algorithm which computes, for a kinematic point mass moving in the plane, a time-optimal path that visits a sequence of target sets while conservatively avoiding collision with moving obstacles, also modelled as kinematic point masses, but whose trajectories are unknown. The problem is formulated as a pursuit-evasion differential game, and the underlying construction is based on optimal control. The algorithm, which is a variant of the fast marching method for shortest path problems, can handle general dynamical constraints on the players and arbitrary domain geometry (e.g. obstacles, non-polygonal boundaries). Applications to a two-stage game, capture-the-flag, is presented.

The task of planning and controlling robot motion in practical applications is often complicated by the effects of model uncertainties and environment disturbances. We present in this paper a systematic approach for generating robust motion control strategies to satisfy high level specifications of safety, target attainability, and invariance, under unknown but bounded, continuous disturbances. The motion planning task is decomposed into the two sub-problems of finite horizon reach with avoid and infinite horizon invariance. The set of states for which each of the sub-problems is robustly feasible is computed via iterative reachability calculations under a differential game framework. We discuss how the results of this computation can be used to inform selections of control inputs based upon state measurements at run-time and provide an algorithm for implementing the corresponding feedback control policies. Finally, we demonstrate an experimental application of this method to the control of an autonomous helicopter in tracking a moving ground vehicle.

Capture-the-flag is a complex, challenging game that is a useful proxy for many problems in robotics and other application areas. The game is adversarial, with multiple, potentially competing, objectives. This interplay between different factors makes the problem complex, even in the case of only two players. To make analysis tractable, previous approaches often make various limiting assumptions upon player actions. In this paper, we present a framework for analyzing and solving a two-player capture-the-flag game as a zero-sum differential game. Our problem formulation allows each player to make decisions rationally based upon the current player positions, assuming only an upper bound on the movement speeds. Using Hamilton-Jacobi reachability analysis, we compute winning regions for each player as subsets of the joint configuration space and derive the corresponding winning strategies. Simulation results are presented along with implications of the work as a tool for automation-aided decision-making for humans and mixed human-robot teams.

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.

Quadrotor helicopters have become increasingly important in recent years as platforms for both research and commercial unmanned aerial vehicle applications. This paper extends previous work on several important aerodynamic effects impacting quadrotor flight in regimes beyond nominal hover conditions. The implications of these effects on quadrotor performance are investigated and control techniques are presented that compensate for them accordingly. The analysis and control systems are validated on the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control quadrotor helicopter testbed by performing the quadrotor equivalent of the stall turn aerobatic maneuver. Flight results demonstrate the accuracy of the aerodynamic models and improved control performance with the proposed control schemes.

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.

This paper describes a low-cost experimental platform for investigating control and dynamics of a vehicle performing high speed sliding turns in an off-road environment. The hardware design and field performance of the vehicle are discussed. State and control input data were recorded during a series of human-controlled off-road driving maneuvers. Analysis performed on the data demonstrates the ability to detect slippage and measure sideslip angle. Preliminary classification of human control inputs using pattern recognition techniques shows the ability to match steering inputs with vehicle trajectories that can be used to develop motion primitives for vehicle control. These tools and techniques will be used for the development of high speed autonomous off-road driving.