Nima Ghods

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.

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.

Multi-agent deployment around a source in one dimension by extremum seeking

We consider the problem of deploying a group of autonomous vehicles (agents) in a formation which has higher density near the source of a measurable signal and lower density away from the source. The spatial distribution of the signal and the location of the source are unknown but the signal is known to decay with the distance from the source. The vehicles do not have the capability of sensing their own positions but they are capable of sensing the distance between them and their neighbors. We design a control algorithm based on a combination of two components. One component of the control law is inspired by the heat PDE and it results in the agents deploying between two anchor agents. The other component of the control law is based on extremum seeking and it achieves higher vehicle density around the source. Using averaging theory for PDEs we prove that the vehicle density will be highest around the source. We also quantify the spatial density function. By discretizing the model with respect to the continuous agent index, we obtain decentralized control laws for discrete agents and illustrate the theoretical results with simulations.

Source Seeking With Very Slow or Drifting Sensors

Slow sensors arise in many applications, including sensing chemical concentrations in tracking of contaminant plumes. Slow sensors are often the cause of poor performance and a potential cause of instability. In this paper, we design a modified extremum seeking scheme to account and exploit slow sensor dynamics. We also consider the worst case, which is sensor dynamics governed by a pure integrator. We provide stability results for several distinct variations of an extremum seeking scheme for one-dimensional optimization. Then we develop a design for source seeking in a plane using a fully actuated vehicle, prove its closed-loop convergence, and present simulation results. We use metal oxide microhotplate gas sensors as a real world example of slow sensor dynamics, model the sensor based on experimental data, and employ the identified sensor model in our source seeking simulations.

3D nonholonomic source seeking without position measurement

We consider the three dimensional problem of directing a nonholonomic vehicle to seek the source of a scalar signal without the use of position information. If we assume the signal strength decays with distance from the source then we achieve convergence to the source by making use of the extremum seeking method. In the kinematic vehicle model we employ, the forward velocity is constrained to a constant and the control inputs are the yaw and pitch velocities. We present a control scheme which tunes these angular velocities and prove the local exponential convergence of this scheme. We also provide simulations which illustrate the behavior of the vehicle under different scenarios, such as static and moving sources, signal fields with spherical and elliptical level sets and parameter regimes not covered by theory.

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.

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.

Localization of remote odor sources by metal-oxide gas sensors in turbulent plumes

Numerous applications reported in the sensors literature have established metal-oxide gas sensors as effective devices for detecting and quantifying a broad range of chemical events. A critical question that could substantially expand their usage is the following: can they characterize the spatio-temporal stimulus characteristics for predicting the source location? We show that commercially-available metal-oxide sensors have a high enough temporal resolution for such a characterization. By selecting proper features of the sensor response and by maintaining a representative response database recorded from known locations in similar plumes, simple short-time measurements can accurately predict the displacement from the source to the sensing location. A key advantage of such a prediction scheme is its achieving the localization remotely and without a navigation within the plume.

Extremum seeking with very slow or drifting sensors

Slow sensors arise in many applications, including sensing of concentrations of chemicals in tracking of contaminant plumes. Slow sensors are often the cause of poor performance and a potential cause of instability. In this paper we design a modified extremum seeking scheme to account for and even to exploit slow sensor dynamics. We also consider the worst case, which is sensor dynamics governed by a pure integrator. We provide stability results for several distinct variations on our ES scheme. We use metal-oxide microhotplate gas sensors as a real world example of slow sensor dynamics, model the sensor based on experimental data, and provide extremum seeking simulation results employing the identified sensor model.

Source Seeking for Nonholonomic Unicycle With Speed Regulation

The simplest strategy for extremum seeking-based source localization, for sources with unknown spatial distributions and nonholonomic unicycle vehicles without position measurement, employs a constant positive forward speed. Steering of the vehicle in the plane is performed using only the variation of the angular velocity. While keeping the forward speed constant is a reasonable strategy motivated by implementation with aerial vehicles, it leads to complexities in the asymptotic behavior of the vehicle, since the vehicle cannot settle—at best it can converge to a small-size attractor around the source. In this paper we regulate the forward velocity, with the intent of bringing the vehicle to a stop, or as close to a stop as possible. The vehicle speed is controlled using simple derivative-like feedback of the sensor measurement (the derivative is approximated with a washout filter) to which a speed bias parameter Vc is added. The angular velocity is tuned using standard extremum seeking. We prove two results. For Vc in a certain range around zero, we show that the vehicle converges to a ring around the source and on average the limit of the vehicle’s heading is either directly away or towards the source. For other values of Vc > 0, the vehicle converges to a ring around the source and it revolves around the source. Interestingly, the average heading of this revolution around the source is more outward than inward—this is possible because the vehicle’s speed is not constant, it is lower during the outward steering intervals and higher during the inward steering intervals. The theoretical results are illustrated with simulations.© 2010 ASME