Claire J. Tomlin

Conflict resolution for air traffic management: a study in multiagent hybrid systems

Air traffic management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe conflict resolution manoeuvres. The method models the aircraft and the manoeuvre as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft. Examples of manoeuvres using both speed and heading changes are worked out in detail.

Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment

Quadrotor helicopters are emerging as a popular platform for unmanned aerial vehicle (UAV) research, due to the simplicity of their construction and maintenance, their ability to hover, and their vertical take o and landing (VTOL) capability. Current designs have often considered only nominal operating conditions for vehicle control design. This work seeks to address issues that arise when deviating significantly from the hover flight regime. Aided by well established research for helicopter flight control, three separate aerodynamic eects are investigated as they pertain to quadrotor flight, due to vehicular velocity, angle of attack, and airframe design. They cause moments that aect attitude control, and thrust variation that aects altitude control. Where possible, a theoretical development is first presented, and is then validated through both thrust test stand measurements and vehicle flight tests using the Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC) quadrotor helicopter. The results enabled improved controller performance.

Controllers for reachability specifications for hybrid systems

The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we refer to as safety). The system performance with respect to lower priority objectives (which we refer to as efficiency) can then be optimized within this class. We motivate our approach by showing how the proposed synthesis technique simplifies to well-known results from supervisory control and pursuit evasion games when restricted to purely discrete and purely continuous systems respectively. We then illustrate the application of this technique to two examples, one hybrid (the steam boiler benchmark problem), and one primarily continuous (a flight vehicle management system with discrete flight modes).

A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

We describe and implement an algorithm for computing the set of reachable states of a continuous dynamic game. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques for computing the reachable set have been proposed, the differential game formulation allows treatment of nonlinear systems with inputs and uncertain parameters. Because the time-dependent equations solution is continuous and defined throughout the state space, methods from the level set literature can be used to generate more accurate approximations than are possible for formulations with potentially discontinuous solutions. A numerical implementation of our formulation is described and has been released on the web. Its correctness is verified through a two vehicle, three dimensional collision avoidance example for which an analytic solution is available.

Computational techniques for the verification of hybrid systems

Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances, analyses, and numerical tools are needed. In this paper, we first present a general model for a hybrid system along with an overview of methods for verifying continuous and hybrid systems. We describe a particular verification technique for hybrid systems, based on two-person zero-sum game theory for automata and continuous dynamical systems. We then outline a numerical implementation of this technique using level set methods, and we demonstrate its use in the design and analysis of aircraft collision avoidance protocols and in verification of autopilot logic.

Aerodynamics and control of autonomous quadrotor helicopters in aggressive maneuvering

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 (STARMAC)

As an alternative to cumbersome aerial vehicles with considerable maintenance requirements and flight envelope restrictions, the X4 flyer is chosen as the basis for the Stanford testbed of autonomous rotorcraft for multi-agent control (STARMAC). This paper outlines the design and development of a miniature autonomous waypoint tracker flight control system, and the creation of a multi-vehicle platform for experimentation and validation of multi-agent control algorithms. This testbed development paves the way for real-world implementation of recent work in the fields of autonomous collision and obstacle avoidance, task assignment formation flight, using both centralized and decentralized techniques.

Decentralized optimization, with application to multiple aircraft coordination

We present a decentralized optimization method for solving the coordination problem of interconnected nonlinear discrete-time dynamic systems with multiple decision makers. The optimization framework embeds the inherent structure in which each decision maker has a mathematical model that captures only the local dynamics and the associated interconnecting global constraints. A globally convergent algorithm based on sequential local optimizations is presented. Under assumptions of differentiability and linear independence constraint qualification, we show that the method results in global convergence to /spl epsiv/-feasible Nash solutions that satisfy the Karush-Kuhn-Tucker necessary conditions for Pareto-optimality. We apply this methodology to a multiple unmanned air vehicle system, with kinematic aircraft models, coordinating in a common airspace with separation requirements between the aircraft.

Quadrotor Helicopter Trajectory Tracking Control

The Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control (STARMAC), a eet of quadrotor helicopters, has been developed as a testbed for novel algorithms that enable autonomous operation of aerial vehicles. This paper develops an autonomous vehicle trajectory tracking algorithm through cluttered environments for the STARMAC platform. A system relying on a single optimization must trade o the complexity of the planned path with the rate of update of the control input. In this paper, a trajectory tracking controller for quadrotor helicopters is developed to decouple the two problems. By accepting as inputs a path of waypoints and desired velocities, the control input can be updated frequently to accurately track the desired path, while the path planning occurs as a separate process on a slower timescale. To enable the use of planning algorithms that do not consider dynamic feasibility or provide feedforward inputs, a computationally ecient algorithm using space-indexed waypoints is presented to modify the speed prole of input paths to guarantee feasibility of the planned trajectory and minimum time traversal of the planned. The algorithm is an ecient alternative to formulating a nonlinear optimization or mixed integer program. Both indoor and outdoor ight test results are presented for path tracking on the STARMAC vehicles.

Level Set Methods for Computation in Hybrid Systems

Reachability analysis is frequently used to study the safety of control systems. We present an implementation of an exact reachability operator for nonlinear hybrid systems. After a brief review of a previously presented algorithm for determining reachable sets and synthesizing control laws--upon whose theory the new implementation rests--an equivalent formulation is developed of the key equations governing the continuous state reachability. The new formulation is implemented using level set methods, and its effectiveness is shown by the numerical solution of three examples.