Showing papers presented at "American Control Conference in 2007"

Autonomous Automobile Trajectory Tracking for Off-Road Driving: Controller Design, Experimental Validation and Racing

Abstract: This paper presents a nonlinear control law for an automobile to autonomously track a trajectory, provided in real-time, on rapidly varying, off-road terrain. Existing methods can suffer from a lack of global stability, a lack of tracking accuracy, or a dependence on smooth road surfaces, any one of which could lead to the loss of the vehicle in autonomous off-road driving. This work treats automobile trajectory tracking in a new manner, by considering the orientation of the front wheels - not the vehicle's body - with respect to the desired trajectory, enabling collocated control of the system. A steering control law is designed using the kinematic equations of motion, for which global asymptotic stability is proven. This control law is then augmented to handle the dynamics of pneumatic tires and of the servo-actuated steering wheel. To control vehicle speed, the brake and throttle are actuated by a switching proportional integral (PI) controller. The complete control system consumes a negligible fraction of a computer's resources. It was implemented on a Volkswagen Touareg, "Stanley", the Stanford Racing Team's entry in the DARPA Grand Challenge 2005, a 132 mi autonomous off-road race. Experimental results from Stanley demonstrate the ability of the controller to track trajectories between obstacles, over steep and wavy terrain, through deep mud puddles, and along cliff edges, with a typical root mean square (RMS) crosstrack error of under 0.1 m. In the DARPA National Qualification Event 2005, Stanley was the only vehicle out of 40 competitors to not hit an obstacle or miss a gate, and in the DARPA Grand Challenge 2005 Stanley had the fastest course completion time.

A Tutorial on the Mechanisms, Dynamics, and Control of Atomic Force Microscopes

Abstract: The atomic force microscope (AFM) is one of the most versatile tools in nanotechnology. For control engineers this instrument is particularly interesting, since its ability to image the surface of a sample is entirely dependent upon the use of a feedback loop. This paper will present a tutorial on the control of AFMs. We take the reader on a walk around the control loop and discuss each of the individual technology components. The major imaging modes are described from a controls perspective and recent advances geared at increasing the performance of these microscopes are highlighted.

Finite-Time Distributed Consensus in Graphs with Time-Invariant Topologies

Abstract: We present a method for achieving consensus in distributed systems in a finite number of time-steps. Our scheme involves a linear iteration where, at each time-step, each node updates its value to be a weighted average of its own previous value and those of its neighbors. If D denotes the degree of the minimal polynomial of the weight matrix associated with the linear iteration, we show that each node can immediately calculate the consensus value as a linear combination of its own past values over at most D time-steps. We also show that each node can determine the coefficients for this linear combination in a decentralized manner. The proposed scheme has the potential to significantly reduce the time and communication required to reach consensus in distributed systems.

Sliding Mode Observer and Backstepping Control for a Quadrotor Unmanned Aerial Vehicles

Abstract: In this paper, we propose a new approach of the backstepping control running parallel with a sliding mode observer for a quadrotor unmanned aerial vehicle. The sliding mode observer works as an observer of the quadrotor velocities and estimator of the external disturbances such as wind and parameter uncertainties. The controller objective is to achieve good tracking of desired (x,y,z) absolute positions and yaw angle while keeping the stability of the pitch and roll angles, in spite of the presence of bounded external disturbances. For this reason, the observer-controller is proposed to estimate the effect of external perturbations in order to compensate them. The design methodology is based on Lyapunov stability. Simulation results show the good performances and the robustness of the proposed observer-controller.

Distributed Tracking for Mobile Sensor Networks with Information-Driven Mobility

Abstract: In this paper, we address distributed target tracking for mobile sensor networks using the extension of a distributed Kalman filtering (DKF) algorithm introduced by the author in [11]. It is shown that improvement of the quality of tracking by mobile sensors (or agents) leads to the emergence of flocking behavior. We discuss the benefits of a flocking-based mobility model for distributed Kalman filtering over mobile networks. This mobility model uses author's flocking algorithm with a natural choice of a moving rendezvous point that is the target itself. As the agents "flock" towards the target, the information value of their sensor measurements improves in time. During this process, smaller flocks merge and form larger flocks and eventually a single flock with a connected topology emerges. This allows the agents to perform cooperative filtering using the DKF algorithm which considerably improves their tracking performance. We show that this flocking algorithm is in fact an information-driven mobility that acts as a cooperative control strategy that enhances the aggregate information value of all sensor measurements. A metric for information value is given that has close connections to Fisher information. Simulation results are provided for a group of UAVs with embedded sensors tracking a mobile target using cooperative filtering.

String Stability Analysis for Heterogeneous Vehicle Strings

Abstract: The spacing errors of a string stable, homogeneous vehicle string attenuate uniformly down the vehicle chain. This result is useful for implementing vehicle formation control because it provides a guideline for the proper intervehicle spacing. In the heterogeneous case, the differing dynamics of the vehicles means the spacing errors do not attenuate or amplify uniformly down the vehicle chain, regardless of whether the formation is string stable or not. Questions arise regarding how heterogeneous string stability should be defined, and what should the proper intervehicle spacing be in order to guarantee nominal safety. In this paper, heterogeneous vehicle strings under simple decentralized control laws with the constant spacing control policy are analyzed. A definition for heterogeneous string stability is proposed. The necessary and sufficient conditions for heterogeneous string stability are given for the constant spacing leader-predecessor following control strategy. The scalability of the control scheme is verified by analyzing the worst case disturbance to error gain. It is shown that string stability can be achieved for heterogeneous vehicle strings of arbitrary length and arbitrary vehicle type ordering.

Autonomous Searching and Tracking of a River using an UAV

Abstract: Surveillance operations include inspecting and monitoring river boundaries, bridges and coastlines. An autonomous unmanned aerial vehicle (UAV) can decrease the operational costs, expedite the monitoring process and be used in situations where a manned inspection is not possible. This paper addresses the problem of searching and mapping such littoral boundaries using an autonomous UAV based on visual feedback. Specifically, this paper describes an exploration system that equips a fixed wing UAV to autonomously search a given area for a specified structure (could be a river, a coastal line etc.), identify the structure if present and map the coordinates of the structure based on the images from the onboard sensor(could be vision or near infra-red). Experimental results with a fixed wing UAV searching and mapping the coordinates of a 2 mile stretch of a river with a cross track error of around 9 meters are presented.

Lyapunov-based Model Predictive Control of Nonlinear Systems Subject to Data Losses

Abstract: In this work, we focus on control of nonlinear systems subject to data losses. In order to regulate the state of the system towards an equilibrium point while minimizing a given performance index, we propose a Lyapunov-based model predictive controller which is designed taking data losses explicitly into account, both in the optimization problem formulation and in the controller implementation.

Guaranteed Transient Performance with L1 Adaptive Controller for Systems with Unknown Time-varying Parameters and Bounded Disturbances: Part I

Abstract: This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbances. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation rate. Simulations of a robotic arm with time-varying friction verify the theoretical findings.

A Graph-Theoretic Characterization of Controllability for Multi-agent Systems

Abstract: In this paper, we continue our pursuit of conditions that render a multi-agent networked system controllable. In particular, such conditions are sought for networks in which a collection of the agents take on leader roles while the remaining agents execute local, consensus-like control laws. Equitable partitions are introduced in order to improve on previous controllability results and the main contribution of this paper is a new necessary condition for controllability.

Control of constrained positive discrete systems

Abstract: Stabilization problem of positive discrete-time systems with bounds on the inputs or the states is solved in this paper. First, the synthesis of state-feedback controllers that ensure the nonnegativity and the stability of the unconstrained closed-loop systems is studied for both the nominal and uncertain systems. These results are then extended to the case of bounded controls and also for systems with bounds on the states. All the proposed conditions are solvable in terms of Linear Programming. A cost function is then proposed to synthesis controllers with good performance. An example illustrate the feasibility of the proposed approach.

Stability Margins of L 1 Adaptive Controller: Part II

Abstract: In [1], we present a novel L1 adaptive control architecture that enables fast adaptation and leads to uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. In this paper, we derive the stability margins of it and verify those in simulations.

Extended Kalman Filter for State Estimation and Trajectory Prediction of a Moving Object Detected by an Unmanned Aerial Vehicle

Abstract: The development of effective target tracking and collision avoidance algorithms is essential to the success of unmanned aerial vehicle (UAV) missions. In a dynamic environment, path planning for UAVs is often based on predicted obstacle and target motion. In this paper, an extended Kalman filter (EKF) is first used to estimate the states of a moving object detected by a UAV from its measured position in space. The optimal object trajectory is then predicted from the estimated object states and using the motion model defined for Kalman filtering. Finally, the quality of the predicted trajectory is evaluated by computing the variance of the prediction error. Simulation results are presented to demonstrate the effectiveness of the proposed approach.

Identification for gain-scheduling: a balanced subspace approach

Abstract: The problem of deriving MIMO parameter- dependent models for gain-scheduling control design from data generated by local identification experiments is considered and a numerically sound approach is proposed, based on subspace identification ideas combined with the use of suitable properties of balanced state space realisations. Simulation examples are used to demonstrate the performance of the proposed approach.

Second-order Consensus Algorithm with Extensions to Switching Topologies and Reference Models

Abstract: In this paper, we extend the consensus algorithm for double integrator dynamics to the case that the information exchange topologies switch randomly with time and to the case that the final consensus value evolves according to a given nonlinear reference model We show sufficient conditions under which consensus is reached under switching directed information exchange topologies Unlike the consensus algorithm for single integrator dynamics, more stringent conditions are required to guarantee consensus under switching directed topologies in the case of the consensus algorithm for double integrator dynamics In addition, we propose consensus algorithms so that the information variables of each vehicle approach the solution of a nonlinear reference model when only a portion of the vehicles in the team have access to the model

Embedding Health Management into Mission Tasking for UAV Teams

Abstract: Coordinated multi-vehicle autonomous systems can provide incredible functionality, but off-nominal conditions and degraded system components can render this capability ineffective. This paper presents techniques to improve mission-level functional reliability through better system self-awareness and adaptive mission planning. In particular, we extend the traditional definition of health management, which has historically referred to the process of actively monitoring and managing vehicle sub-systems (e.g., avionics) in the event of component failures, to the context of multiple vehicle operations and autonomous multi-agent teams. In this case, health management information about each mission system component is used to improve the mission system's self-awareness and adapt vehicle, guidance, task and mission plans. This paper presents the theoretical foundations of our approach and recent experimental results on a new UAV testbed.

Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations

Abstract: A dynamical sliding-mode control is used to avoid different bit sticking problems present in a conventional vertical oilwell drillstring. The control goal of driving the rotary velocities of drillstring components to a constant positive value is achieved by means of this control. A discontinuous lumped- parameter torsional model of four degrees of freedom is considered. This model allows to describe drill pipes and drill collars behavior. The closed-loop system has two discontinuity surfaces. One of them gives rise to self-excited bit stick-slip oscillations and bit sticking phenomena. The other surface is introduced to accomplish the control goal despite variations in the weight on the bit (key to the dynamics) and other system parameters.

A Constant Factor Approximation Algorithm for Event-Based Sampling

Abstract: We consider a control system in which sensor data is transmitted from the plant to a receiver over a communication channel, and the receiver uses the data to estimate the state of the plant. Using a feedback policy to choose when to transmit data, the goal is to schedule transmissions to balance a trade-off between communication rate and estimation error. Computing an optimal policy for this problem is generally computationally intensive. Here we provide a simple algorithm for computing a suboptimal policy for scheduling state transmissions which incurs a cost within a factor of six of the optimal achievable cost.

A Sum of Squares Approach to Stability Analysis of Polynomial Fuzzy Systems

Abstract: This paper presents a sum of squares (SOS) approach to stability analysis of polynomial fuzzy systems. Our SOS approach provides two innovative and extensive results for the existing LMI approaches to Takagi-Sugeno fuzzy systems. First, we propose a polynomial fuzzy model that is a more general representation of the well-known Takagi-Sugeno fuzzy model. Second, we derive stability conditions based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, stability analysis discussed in this paper is more general than that based on the existing LMI approaches to Takagi-Sugeno fuzzy systems. The stability conditions in the proposed approach can be represented in terms of SOS and are numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, two analytical examples are provided. The first example shows that our approach provides more relaxed stability results than both the existing LMI approaches and a polynomial system approach. The second example illustrates the utility of our approach in comparison with a piecewise Lyapunov function approach.

Lyapunov Guidance Vector Fields for Unmanned Aircraft Applications

Abstract: This paper presents results implementing Lyapunov vector fields for the guidance of unmanned aircraft. The vector fields yield globally stable tracking of circular loiter patterns. These loiter patterns are used in several unmanned aircraft applications including hierarchical micro air vehicle control for cooperative plume tracking, extremum seeking for electronic chaining, and cooperative tracking of moving targets. Extensions of the basic LGVF approach are made for each application including: warping the circular pattern to form other closed orbit patterns; driving the center of the LGVF orbit using virtual dynamics; and spacing multiple unmanned aircraft around a circular orbit. Hardware-in-the- loop simulation results and flight data are given to validate performance.

Packetized Predictive Control over Erasure Channels

Abstract: In digital networked control systems links between controller and plant are not transparent, but are affected by time-delays, data-dropouts and quantization. An important observation is that, in contemporary communication networks, such as those employing Ethernet, data is sent in large packets. This motivates the development of networked control schemes where signal predictions are sent as packets. In the present work we present such a strategy. We focus on a configuration where the controller output is connected to the plant input via a network which we assume is prone to transmission errors. By using methods from predictive control theory, we show how closed loop stability can be ensured directly in the design.

Micro UAV Path Planning for Reconnaissance in Wind

Abstract: The problem addressed in this paper is the control of a micro unmanned aerial vehicle (MAV) for the purpose of obtaining video footage of a set of known ground targets with preferred azimuthal viewing angles, using fixed onboard cameras. Control is exercised only through the selection of waypoints, without modification of the MAV's pre-existing autopilot and waypoint following capability. Specifically, we investigate problems and potential solutions of performing this task in the presence of a known constant wind. Simulations are provided in the presence of randomly perturbed wind, based on the Air Force Research Laboratory equipment and the high fidelity simulator MultiUAV2.

Control of a Quadrotor Vehicle Using Sliding Mode Disturbance Observer

Abstract: This paper uses the recently developed sliding mode control driven by sliding mode disturbance observer approach to design a robust flight controller for a small quadrotor vehicle. This technique allows for continuous control robust to external disturbance and model uncertainties to be computed without the use of high control gain or extensive computational power. The multiple-loop, multiple time-scale flight controller is designed to provide robust position and attitude control of the vehicle while relying only on knowledge of the limits of the disturbances. Extensive simulations of a 6 DOF computer model demonstrate the robustness of the control when faced with external disturbances (including wind, collision and actuator failure) as well as model uncertainties.

Adaptive Control of 3DOF Motion for LAAS Helicopter Benchmark: Design and Experiments

Abstract: The problem of 3DOF motion control for Quanser/LAAS "Helicopter Benchmark" laboratory setup is considered Based on the passification design method and the Implicit Reference Model approach, the adaptive control laws are designed and experimentally tested The MATLAB/Simulink and WinCon software environments are used for adaptive control laws implementation and conducting the real-world experiments The experimental results demonstrate high closed loop system performance and robustness of the suggested control laws with respect to parametric uncertainties and unmodeled plant dynamics and external disturbances An important advantage of adaptive control is simplicity of the design procedure compared to conventional model based approach

On Input-to-State Stability for Nonlinear Systems with Delayed Feedbacks

Abstract: We analyze a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions are both known. We prove that the closed loop systems are input-to-state stable (ISS) relative to actuator errors when small time delays are introduced in the feedbacks. We explicitly construct ISS Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the known Lyapunov functions for the original undelayed closed-loop dynamics. We also provide a general result on ISS for cascade systems with delays. We demonstrate the efficacy of our results using a generalized pendulum dynamics and other examples.

LMI control design for a class of exponential uncertain systems with application to network controlled switched systems

Abstract: This paper is dedicated to the stabilizability of discrete uncertain systems with exponential uncertainties. Such uncertain system are encountered in many application domains that use sampled-data controllers and communication networks. For the sake of generality, the design problem is presented in the context of switched systems. LMI robust control synthesis based on an equivalent polytopic model with an additive norm bounded term are presented. The results are applied to network controlled switched systems in which both the switching signal and the control input are affected by networked induced delay.

Decentralized Control of Unmanned Aerial Vehicle Collaborative Sensing Missions

Abstract: Cooperative unmanned aerial vehicle (UAV) teams can serve as a mobile sensor networks to autonomously execute sensing tasks in uncertain and dynamic environments. We have implemented a UAV system that performs collaborative sensing missions under the supervision of a single user. Decentralized task allocation and autonomous mission execution are enabled by onboard computing and ad-hoc wireless communication and provide robustness to communication and resource losses in quickly evolving scenarios. The collaboration algorithm combines shared and local information to produce multi-step plans with the goal of minimizing the global cost of the mission. Missions are constructed in real time from tasks such as patrolling an area or searching for an intruder, and may include constraints such as a restricted airspace. Algorithms for decentralized planning, guaranteed search and avoiding a restricted airspace were demonstrated using a team of four UAVs. Experimental data shows that tasks were allocated to the appropriate UAVs and successfully executed.

Combined Feedforward/Feedback Control of Atomic Force Microscopes

Abstract: The atomic force microscope (AFM) is a powerful imaging and nanofabrication tool that allows the user to observe and manipulate samples at the atomic level. However, one limitation of current AFMs is the long time required to obtain a quality image of a sample. Several researchers have investigated this problem in recent years, and we give an overview of the approaches explored, including Hinfin, lscr1, and model-inverse based methods. We compare and discuss advantages and disadvantages of the various approaches, and we end with a summary of open questions to be addressed in improving the control of AFMs.

Distributed Sequential Auctions for Multiple UAV Task Allocation

Abstract: Allocating tasks efficiently to multiple UAVs with limited sensor and communication ranges is a difficult problem. In this paper, we present a distributed sequential auction scheme that takes the UAV limitations into account and provides a systematic procedure for the auction process. The task allocation scheme first validates the targets using neighbor's knowledge and then, depending on the decisions obtained from neighbors, an agent decides to auction or forfeit the target. The targets detected within a sensor range are validated and auctioned sequentially. A simulation study was conducted for different sensor and communication ranges to evaluate the performance of the sequential auction scheme which was compared with a greedy strategy and a simple distributed auction scheme. The results show that the sequential auction scheme performs better than the simple distributed auction and greedy strategy.

An Evasive Maneuvering Algorithm for UAVs in See-and-Avoid Situations

Abstract: In this paper, we present an collision avoidance algorithm for unmanned aerial vehicles (UAVs) based on model predictive control. When a UAV encounters other aircraft that is estimated to approach closer than the minimum safety margin, the vehicle must execute an emergency evasive maneuver to avoid the impending collision at all cost. During this procedure, the unmanned vehicle must compute in real time a safe and plausible trajectory based on the collected information on the predicted future path of other vehicles. During the evasive maneuver, the trajectory generation and control problem is very stringent since the conflict-free trajectory must be plausible with respect to the given vehicle dynamics with limited control input. Therefore, in this research, we propose a model predictive control-based trajectory planner to satisfy the requirements listed so far due to its capability to explicitly address the control problem of constrained nonlinear dynamic systems. We consider a few scenarios involving nearby flying objects with various velocity and incident angle conditions. The proposed algorithm is validated in a head-on collision scenario using unmanned aerial vehicles.