Haomiao Huang

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.

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.

Design of guaranteed safe maneuvers using reachable sets: Autonomous quadrotor aerobatics in theory and practice

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.

Applications of hybrid reachability analysis to robotic aerial vehicles

The control of complex non-linear systems can be aided by modeling each system as a collection of simplified hybrid modes, with each mode representing a particular operating regime defined by the system dynamics or by a region of the state space in which the system operates. Guarantees on the safety and performance of such hybrid systems can still be challenging to generate, however. Reachability analysis using a dynamic game formulation with Hamilton—Jacobi methods provides a useful way to generate these types of guarantees, and the technique is flexible enough to analyze a wide variety of systems. This paper presents two applications of reachable sets, both focused on guaranteeing the safety and performance of robotic aerial vehicles. In the first example, reachable sets are used to design and implement a backflip maneuver for a quadrotor helicopter. In the second, reachability analysis is used to design a decentralized collision avoidance algorithm for multiple quadrotors. The theory for both examples is explained, and successful experimental results are presented from flight tests on the STARMAC quadrotor helicopter platform.

Guaranteed decentralized pursuit-evasion in the plane with multiple pursuers

Pursuit-evasion games are an important problem in robotics and control, but games with many players are difficult to analyze and solve. This paper studies a game of multiple pursuers cooperating to capture a single evader in a bounded, convex, polytope in the plane. We present a decentralized control scheme based on the Voronoi partion of the game domain, where the pursuers jointly minimize the area of the evaders Voronoi cell. We prove that capturing the evader is guaranteed under this scheme regardless of the evaders actions, and show simulation results demonstrating the pursuit strategy.

A differential game approach to planning in adversarial scenarios: A case study on capture-the-flag

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.

Reachability-based synthesis of feedback policies for motion planning under bounded disturbances

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.

Time-optimal multi-stage motion planning with guaranteed collision avoidance via an open-loop game formulation

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.

A general, open-loop formulation for reach-avoid games

A reach-avoid game is one in which an agent attempts to reach a predefined goal, while avoiding some adversarial circumstance induced by an opposing agent or disturbance. Their analysis plays an important role in problems such as safe motion planning and obstacle avoidance, yet computing solutions is often computationally expensive due to the need to consider adversarial inputs. In this work, we present an open-loop formulation of a two-player reach-avoid game whereby the players define their control inputs prior to the start of the game. We define two open-loop games, each of which is conservative towards one player, show how the solutions to these games are related to the optimal feedback strategy for the closed-loop game, and demonstrate a modified Fast Marching Method to efficiently compute those solutions.

Design and Analysis of Hybrid Systems, with Applications to Robotic Aerial Vehicles

Decomposing complex, highly nonlinear systems into aggregates of simpler hybrid modes has proven to be a very successful way of designing and controlling autonomous vehicles. Examples include the use of motion primitives for robotic motion planning and equivalently the use of discrete maneuvers for aggressive aircraft trajectory planning. In all of these approaches, it is extremely important to verify that transitions between modes are safe. In this paper, we present the use of a Hamilton-Jacobi differential game formulation for finding continuous reachable sets as a method of generating provably safe transitions through a sequence of modes for a quadrotor performing a backflip maneuver.