Prescribed-Time Seeking of a Repulsive Source by Unicycle Angular Velocity Tuning

All the existing source seeking algorithms for unicycle models in GPS-denied settings guarantee at best an exponential rate of convergence over an infinite interval. Using the recently introduced time-varying feedback tools for prescribed-time stabilization, we achieve source seeking in prescribed time, i.e., the convergence to the source, without the measurements of the position and velocity of the unicycle, in as short a time as the user desires, starting from an arbitrary distance from the source. The convergence is established using a singularly perturbed version of the Lie bracket averaging method, combined with time dilation and time contraction operations. The algorithm is robust, provably, even to an arbitrarily strong gradient-dependent repulsive velocity drift emanating from the source

Coverage and Field Estimation on Bounded Domains by Diffusive Swarms

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016

Optimized state feedback regulation of 3DOF helicopter system via extremum seeking

In this paper, an optimized state feedback regulation of a 3 degree of freedom (DOF) helicopter is designed via extremum seeking (ES) technique. Multi-parameter ES is applied to optimize the tracking performance via tuning State Vector Feedback with Integration of the Control Error (SVFBICE). Discrete multivariable version of ES is developed to minimize a cost function that measures the performance of the controller. The cost function is a function of the error between the actual and desired axis positions. The controller parameters are updated online as the optimization takes place. This method significantly decreases the time in obtaining optimal controller parameters. Simulations were conducted for the online optimization under both fixed and varying operating conditions. The results demonstrate the usefulness of using ES for preserving the maximum attainable performance

Optimization based solutions for control and state estimation in non-holonomic mobile robots: stability, distributed control, and relative localization

Interest in designing, manufacturing, and using autonomous robots has been rapidly growing during the most recent decade. The main motivation for this interest is the wide range of potential applications these autonomous systems can serve in. The applications include, but are not limited to, area coverage, patrolling missions, perimeter surveillance, search and rescue missions, and situational awareness. In this thesis, the area of control and state estimation in non-holonomic mobile robots is tackled. Herein, optimization based solutions for control and state estimation are designed, analyzed, and implemented to such systems. One of the main motivations for considering such solutions is their ability of handling constrained and nonlinear systems such as non-holonomic mobile robots. Moreover, the recent developments in dynamic optimization algorithms as well as in computer processing facilitated the real-time implementation of such optimization based methods in embedded computer systems. Two control problems of a single non-holonomic mobile robot are considered first; these control problems are point stabilization (regulation) and path-following. Here, a model predictive control (MPC) scheme is used to fulfill these control tasks. More precisely, a special class of MPC is considered in which terminal constraints and costs are avoided. Such constraints and costs are traditionally used in the literature to guarantee the asymptotic stability of the closed loop system. In contrast, we use a recently developed stability criterion in which the closed loop asymptotic stability can be guaranteed by appropriately choosing the prediction horizon length of the MPC controller. This method is based on finite time controllability as well as bounds on the MPC value function. Afterwards, a regulation control of a multi-robot system (MRS) is considered. In this control problem, the objective is to stabilize a group of mobile robots to form a pattern. We achieve this task using a distributed model predictive control (DMPC) scheme based on a novel communication approach between the subsystems. This newly introduced method is based on the quantization of the robots’ operating region. Therefore, the proposed communication technique allows for exchanging data in the form of integers instead of floating-point numbers. Additionally, we introduce a differential communication scheme to achieve a further reduction in the communication load. Finally, a moving horizon estimation (MHE) design for the relative state estimation (relative localization) in an MRS is developed in this thesis. In this framework, robots with less payload/computational capacity, in a given MRS, are localized and tracked using robots fitted with high-accuracy sensory/computational means. More precisely, relative measurements between these two classes of robots are used to localize the less (computationally) powerful robotic members. As a complementary part of this study, the MHE localization scheme is combined with a centralized MPC controller to provide an algorithm capable of localizing and controlling an MRS based only on relative sensory measurements. The validity and the practicality of this algorithm are assessed by realtime laboratory experiments. The conducted study fills important gaps in the application area of autonomous navigation especially those associated with optimization based solutions. Both theoretical as well as practical contributions have been introduced in this research work. Moreover, this thesis constructs a foundation for using MPC without stabilizing constraints or costs in the area of non-holonomic mobile robots

Reactive Planning With Legged Robots In Unknown Environments

Unlike the problem of safe task and motion planning in a completely known environment, the setting where the obstacles in a robot\u27s workspace are not initially known and are incrementally revealed online has so far received little theoretical interest, with existing algorithms usually demanding constant deliberative replanning in the presence of unanticipated conditions. Moreover, even though recent advances show that legged platforms are becoming better at traversing rough terrains and environments, legged robots are still mostly used as locomotion research platforms, with applications restricted to domains where interaction with the environment is usually not needed and actively avoided. In order to accomplish challenging tasks with such highly dynamic robots in unexplored environments, this research suggests with formal arguments and empirical demonstration the effectiveness of a hierarchical control structure, that we believe is the first provably correct deliberative/reactive planner to engage an unmodified general purpose mobile manipulator in physical rearrangements of its environment. To this end, we develop the mobile manipulation maneuvers to accomplish each task at hand, successfully anchor the useful kinematic unicycle template to control our legged platforms, and integrate perceptual feedback with low-level control to coordinate each robot\u27s movement. At the same time, this research builds toward a useful abstraction for task planning in unknown environments, and provides an avenue for incorporating partial prior knowledge within a deterministic framework well suited to existing vector field planning methods, by exploiting recent developments in semantic SLAM and object pose and triangular mesh extraction using convolutional neural net architectures. Under specific sufficient conditions, formal results guarantee collision avoidance and convergence to designated (fixed or slowly moving) targets, for both a single robot and a robot gripping and manipulating objects, in previously unexplored workspaces cluttered with non-convex obstacles. We encourage the application of our methods by providing accompanying software with open-source implementations of our algorithms

Adaptive Path Following for an Underactuated Nonholonomic Mobile Manipulator

We investigate an adaptive path following problem for an underactuated nonholonomic mobile manipulator system and closed planar curves. As opposed to adapting to uncertain or unknown dynamics in the plant, we apply an adaptation approach with respect to an unknown geometric path. First, we present a solution to the non-adaptive path following problem using the concept of a path following output and apply it to circular and elliptical paths. To overcome a drawback associated with our first proposed solution and set the stage for our approach to the adaptive case, we apply an approximation approach based on osculating circles for strictly convex closed curves. We transition to the adaptive path following case by first presenting an algorithm to estimate unknown path parameters in the case of a circular path. We use our estimation algorithm and our path following solution for circular paths in an indirect adaptive control scheme. Thereafter, again using the osculating circle of a curve and the approximation technique of our second non-adaptive path following solution, we extend our adaptive solution, under some mild assumptions, for unknown strictly convex closed curves in the plane

Safe navigation and motion coordination control strategies for unmanned aerial vehicles

Unmanned aerial vehicles (UAVs) have become very popular for many military and civilian applications including in agriculture, construction, mining, environmental monitoring, etc. A desirable feature for UAVs is the ability to navigate and perform tasks autonomously with least human interaction. This is a very challenging problem due to several factors such as the high complexity of UAV applications, operation in harsh environments, limited payload and onboard computing power and highly nonlinear dynamics. Therefore, more research is still needed towards developing advanced reliable control strategies for UAVs to enable safe navigation in unknown and dynamic environments. This problem is even more challenging for multi-UAV systems where it is more efficient to utilize information shared among the networked vehicles. Therefore, the work presented in this thesis contributes towards the state-of-the-art in UAV control for safe autonomous navigation and motion coordination of multi-UAV systems. The first part of this thesis deals with single-UAV systems. Initially, a hybrid navigation framework is developed for autonomous mobile robots using a general 2D nonholonomic unicycle model that can be applied to different types of UAVs, ground vehicles and underwater vehicles considering only lateral motion. Then, the more complex problem of three-dimensional (3D) collision-free navigation in unknown/dynamic environments is addressed. To that end, advanced 3D reactive control strategies are developed adopting the sense-and-avoid paradigm to produce quick reactions around obstacles. A special case of navigation in 3D unknown confined environments (i.e. tunnel-like) is also addressed. General 3D kinematic models are considered in the design which makes these methods applicable to different UAV types in addition to underwater vehicles. Moreover, different implementation methods for these strategies with quadrotor-type UAVs are also investigated considering UAV dynamics in the control design. Practical experiments and simulations were carried out to analyze the performance of the developed methods. The second part of this thesis addresses safe navigation for multi-UAV systems. Distributed motion coordination methods of multi-UAV systems for flocking and 3D area coverage are developed. These methods offer good computational cost for large-scale systems. Simulations were performed to verify the performance of these methods considering systems with different sizes