Antranik A. Siranosian

Source seeking with non-holonomic unicycle without position measurement and with tuning of forward velocity

We consider the problem of seeking the source of a scalar signal using an autonomous vehicle modeled as the non-holonomic unicycle and equipped with a sensor of that scalar signal but not possessing the capability to sense either the position of the source nor its own position. We assume that the signal field is the strongest at the source and decays away from it. The functional form of the field is not available to our vehicle. We employ extremum seeking to estimate the gradient of the field in real time and steer the vehicle towards the point where the gradient is zero (the maximum of the field, i.e., the location of the source). We employ periodic forward–backward movement of the unicycle (implementable with mobile robots and some underwater vehicles but not with aircraft), where the forward velocity has a tunable bias term, which is appropriately combined with extremum seeking to produce a net effect of “drifting” towards the source. In addition to simulation results we present a local convergence proof via averaging, which exhibits a delicate periodic structure with two sinusoids of different frequencies—one related to the angular velocity of the unicycle and the other related to the probing frequency of extremum seeking.

Brief paper: Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements

We remove the long standing restriction that plant dynamics in extremum seeking (ES) must be stable and provide an extension that allows single integrators, double integrators, and moderately unstable single poles. An application for single and double integrators is in control of autonomous vehicles. ES can be used for finding a source of a signal (chemical, electromagnetic, etc.) whose strength decays with the distance. This can be achieved without the measurement of the position vector and using only the measurement of the scalar signal. Extremum seeking extracts the position information implicit in the scalar measurement and needed for tracking through non-model based gradient estimation

3-D Source Seeking for Underactuated Vehicles Without Position Measurement

Our past work introduced source seeking methods for GPS-denied autonomous vehicles using only local signal measurement and operating in two dimensions. In this paper, we extend these results to three dimensions. The 3D extensions introduce many interesting challenges, including the choice of vehicle models in 3D, sensor placement to allow probing-based gradient estimation of an unknown signal field in 3D, the question of what type of pattern of vehicle motion can be produced in an underactuated 3D vehicle to allow tuning by single-loop or multiloop extremum seeking, and the shape of attractors, which become very complex in 3D. We present two control schemes that address these questions. The first scheme focuses on vehicles with a constant forward velocity and the ability to actuate pitch and yaw velocities. The second scheme employs vehicles with constant forward and pitch velocities and actuate only the roll velocity. Our results include convergence analysis and simulation results.

Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements

We remove the long standing restriction that plant dynamics in extremum seeking (ES) must be stable and provide an extension that allows single integrators, double integrators, and moderately unstable single poles. An application for single and double integrators is in control of autonomous vehicles. ES can be used for finding a source of a signal (chemical, electromagnetic, etc.) whose strength decays with the distance. This can be achieved without the measurement of the position vector and using only the measurement of the scalar signal. Extremum seeking extracts the position information implicit in the scalar measurement and needed for tracking through non-model based gradient estimation.

Control of Strings and Flexible Beams by Backstepping Boundary Control

We present the controller and observer designs for hyperbolic PDE systems. The main ideas are introduced on the example of a wave equation - a model of an undamped, vibrating string. Both a full state feedback boundary controller and a boundary sensor based observer are introduced. The string results are followed by a presentation of controller and observer designs for shear beam and Timoshenko beam models. The flexible systems considered in this paper allow the presence of a source of instability at the uncontrolled end of the string/beam. This result is of relevance to control of cantilevered beams in atomic force microscopy where the piezo actuator and the van der Waals forces act on the opposite ends of the beam.

Source seeking with a nonholonomic unicycle without position measurements and with tuning of angular velocity — Part II: Applications

For Part I see ibid. (2007). We present results for autonomous vehicles operating in GPS-denied environments while performing several different tasks. These vehicles employ extensions of extremum seeking to accomplish their goals. Previously, extremum seeking has successfully been applied to vehicles seeking the source of some signal, while operating in such environments. This paper considers the objectives of tracking a diffusive signal, tracing a level set of a signal field, and modification of the algorithm for use on a vehicle with limited movement capabilities. We present each scenario, detail each control scheme and, in addition, present simulation results.

Gain Scheduling-Inspired Boundary Control for Nonlinear Partial Differential Equations

We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with an in-domain nonlinearity is considered first. For this system a nonlinear feedback law, based on gain scheduling, is derived explicitly, and a proof of local exponential stability, with an estimate of the region of attraction, is presented for the closed-loop system. Control designs (without proofs) are then presented for a string PDE and a shear beam PDE, both with Kelvin–Voigt (KV) damping and free-end nonlinearities of a potentially destabilizing kind. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization based design. [DOI: 10.1115/1.4004065]

GPS denied source seeking for underactuated autonomous vehicles in 3D

Extremum seeking has been successfully applied to source seeking for autonomous vehicles operating in two dimensions. In this paper we extend these results to vehicles operating in three dimensions. The extension is interesting for several reasons. First, there is the choice of vehicle models to consider, and second there is the question of what type of vehicle movement can be actuated. We present two control schemes which address these questions. The first scheme focuses on vehicles with a constant forward velocity and the ability to actuate pitch and yaw velocities. The second scheme explores vehicles which operate with a constant forward velocity and a constant pitch velocity and which are capable of actuating only the roll velocity. We present the vehicle models, details of the control schemes, and simulation results.

Motion planning and tracking for tip displacement and deflection angle for flexible beams

We present results for motion planning and tracking for flexible beams with Kelvin-Voigt damping, when the goal is to track sinusoidal reference signals for the displacement and deflection angle at the free-end of the beam using only actuation at the base. We present the solution to the motion planning problem for the string model, and a method of leveraging the string solution with PDE backstepping theory to solve the motion planning problem for the shear beam. We then present state-feedback boundary controllers that stabilize their respective systems around the motion planning solution.

Gain Scheduling-Inspired Control for Nonlinear Partial Differential Equations

We present a control design method for nonlinear partial differential equations (PDEs) based on a combination of gain scheduling and backstepping theory for linear PDEs. A benchmark first-order hyperbolic system with a destabilizing in-domain nonlinearity is considered first. For this system a nonlinear feedback law based on gain scheduling is derived explicitly, and a statement of stability is presented for the closed-loop system. Control designs are then presented for a string and shear beam PDE, both with Kelvin-Voigt damping and potentially destabilizing free-end nonlinearities. String and beam simulation results illustrate the merits of the gain scheduling approach over the linearization-based design.Copyright