Ashwin P. Dani

Network Connectivity Preserving Formation Stabilization and Obstacle Avoidance via a Decentralized Controller

A decentralized control method is developed to enable a group of agents to achieve a desired global configuration while maintaining global network connectivity and avoiding obstacles, using only local feedback and no radio communication between the agents for navigation. By modeling the interaction among the agents as a graph, and given a connected initial graph with a desired neighborhood between agents, the developed method ensures the desired communication links remain connected for all time. To guide the agents to a desired configuration while avoiding obstacles, a decentralized controller is developed based on the navigation function formalism. By proving that the proposed controller is a qualified navigation function, convergence to the desired formation is guaranteed.

Single Camera Structure and Motion

A reduced order nonlinear observer is proposed for the problem of “structure and motion (SaM)” estimation of a stationary object observed by a moving calibrated camera. In comparison to existing work which requires some knowledge of the Euclidean geometry of an observed object or full knowledge of the camera motion, the developed reduced order observer only requires one camera linear velocity and corresponding acceleration to asymptotically identify the Euclidean coordinates of the feature points attached to an object (with proper scale reconstruction) and the remaining camera velocities. The unknown linear velocities are assumed to be generated using a model with unknown parameters. The unknown angular velocities are determined from a robust estimator which uses a standard Homography decomposition algorithm applied to tracked feature points. A Lyapunov analysis is provided to prove the observer asymptotically estimates the unknown states under a persistency of excitation condition.

Saturated control of an uncertain nonlinear system with input delay

This paper examines saturated control of a general class of uncertain nonlinear systems with time-delayed actuation and additive bounded disturbances. The bound on the control is known a priori and can be adjusted by changing the feedback gains. A Lyapunov-based stability analysis utilizing Lyapunov-Krasovskii (LK) functionals is provided to prove uniformly ultimately bounded tracking despite uncertainties in the dynamics. A numerical example is presented to demonstrate the performance of the controller.

Observer Design for Stochastic Nonlinear Systems via Contraction-Based Incremental Stability

This paper presents a new design approach to nonlinear observers for Itô stochastic nonlinear systems with guaranteed stability. A stochastic contraction lemma is presented which is used to analyze incremental stability of the observer. A bound on the mean-squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity. The observer design is based on a non-unique state-dependent coefficient (SDC) form, which parametrizes the nonlinearity in an extended linear form. The observer gain synthesis algorithm, called linear matrix inequality state-dependent algebraic Riccati equation (LMI-SDARE), is presented. The LMI-SDARE uses a convex combination of multiple SDC parametrizations. An optimization problem with state-dependent linear matrix inequality (SDLMI) constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances. Two variations of LMI-SDARE algorithm are also proposed. One of them named convex state-dependent Riccati equation (CSDRE) uses a chosen convex combination of multiple SDC matrices; and the other named Fixed-SDARE uses constant SDC matrices that are pre-computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre-computed by a convex LMI optimization problem. A connection between contraction analysis and L2 gain of the nonlinear system is established in the presence of noise and disturbances. Results of simulation show superiority of the LMI-SDARE algorithm to the extended Kalman filter (EKF) and state-dependent differential Riccati equation (SDDRE) filter.

Ensuring network connectivity during formation control using a decentralized navigation function

In many applications of formation control, agents coordinate and communicate to make appropriate decisions. Connectivity of the network is paramount in such applications. The goal in this paper is to drive a group of agents with limited sensing capabilities to a desired configuration while ensuring the connectivity of the wireless communication network among the agents. Based on a navigation function formalism, a decentralized cooperative controller is proposed where agent only uses information within its sensing zone to guarantee connectivity maintenance of the network and achieve the desired formation with collision avoidance between themselves and with obstacles in the environment.

Structure and motion estimation of a moving object using a moving camera

A solution is presented to the problem of estimating the structure and motion of a moving object seen from a moving camera. A nonlinear observer is proposed, which asymptotically identifies the structure and motion of the moving object, when the camera motion is persistently exciting. The object is assumed to be moving with constant velocities. The proposed method makes no assumptions on the minimum number of views or point correspondences as required by the existing approaches.

Structure estimation of a moving object using a moving camera: An unknown input observer approach

A state observer is designed for estimating the structure of a moving object with time-varying velocities seen by a moving camera. A nonlinear unknown input observer strategy is used where the objects velocity is considered as an unknown input to the perspective dynamical system. The object is assumed to be moving on a ground plane. The downward-looking camera observing the moving object is also moving (e.g., attached to an air vehicle) with known velocities. The developed method provides the first causal, observer-based structure estimation algorithm for a moving camera viewing a moving object with unknown time-varying object velocities.

Vision-based Localization and Robot-centric Mapping in Riverine Environments

This paper presents a vision-based localization and mapping algorithm developed for an unmanned aerial vehicle (UAV) that can operate in a riverine environment. Our algorithm estimates the three-dimensional positions of point features along a river and the pose of the UAV. By detecting features surrounding a river and the corresponding reflections on the waters surface, we can exploit multiple-view geometry to enhance the observability of the estimation system. We use a robot-centric mapping framework to further improve the observability of the estimation system while reducing the computational burden. We analyze the performance of the proposed algorithm with numerical simulations and demonstrate its effectiveness through experiments with data from Crystal Lake Park in Urbana, Illinois. We also draw a comparison to existing approaches. Our experimental platform is equipped with a lightweight monocular camera, an inertial measurement unit, a magnetometer, an altimeter, and an onboard computer. To our knowledge, this is the first result that exploits the reflections of features in a riverine environment for localization and mapping.

Observer design for stochastic nonlinear systems using contraction analysis

This paper presents a new observer for Itô stochastic nonlinear systems with guaranteed stability. Contraction analysis is used to analyze incremental stability of the observer for an Itô stochastic nonlinear system. A bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of contraction rate and maximum noise intensity. The observer design is based on non-unique state-dependent coefficient (SDC) forms which parametrize the nonlinearity in an extended linear form. In this paper, a convex combination of several parametrizations is used. An optimization problem with state-dependent linear matrix inequality (SDLMI) constraints is formulated to select the free parameters of the convex combination for achieving faster convergence and robustness against disturbances. Moreover, the L2 norm of the disturbance and noise to the estimation error is shown to be finite. The present algorithm shows improved performance in comparison to the extended Kalman filter (EKF) and the state-dependent differential Riccati equation (SDDRE) filter in simulation.

Saturated control of an uncertain Euler-Lagrange system with input delay

This paper examines saturated control of a general class of uncertain nonlinear Euler-Lagrange systems with time-delayed actuation and additive bounded disturbances. The bound on the control is known a priori and can be adjusted by changing the feedback gains. A Lyapunov-based stability analysis utilizing Lyapunov-Krasovskii functionals is provided to prove uniformly ultimately bounded tracking despite uncertainties in the dynamics.