Marcio de Queiroz

Adaptive Nonlinear Control of Multiple Spacecraft Formation Flying

Thispaperconsiderstheproblemofrelativepositioncontrolformultiplespacecraftformatione ying.Specie cally, the full nonlinear dynamics describing the relative positioning of multiple spacecraft formation e ying are used to develop a Lyapunov-based, nonlinear, adaptive control law that guarantees global asymptotic convergence of the position tracking error in the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. Simulation results are included to illustrate the controller performance. that compensated for unknown, constant disturbances while pro- ducing globally asymptotically decaying position tracking errors. This controller, however, required exact knowledge of the space- craft parameters. In this paper we consider the full nonlinear dynamics describ- ing the relative positioning of MSFF for control design purposes. Using Lyapunov-based control design and stability analysis tech- niques, we develop a nonlinear adaptive control law that guarantees global asymptotic convergence of the spacecraft relative position to any sufe ciently smooth desired trajectory, despite the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. In the case when the parameters are ex- actlyknown,theproposedcontrolstrategyyieldsglobalexponential convergence of the tracking errors. In comparison to the work of Refs. 11 and 12, the proposed controller ensures stronger stability resultsandaccountsforawiderclassofparametricuncertainties.As inRefs.11-13, we will consider in this paper the idealized scenario where the spacecraft actuators are capable of providing continuous- time control efforts, as opposed to being of pulse type. 9 We note that the problem of pulse-type, nonlinear control design for MSFF constitutes an open research problem and is beyond the scope of this paper. The paper is organized as follows. Section II presents the non- linear dynamic model derivation. The control objective is stated in Sec. III. The control design and closed-loop stability analysis are presented in Sec. IV. Simulation results are provided in Sec. V, whereas some concluding remarks are given in Sec. VI.

Optimal control, stabilization and nonsmooth analysis

Part I: Optimal Control, Optimization, and Hamilton-Jacobi-Bellman Equations.- Part II: Stabilization and Lyapunov Functions.- Part III: Nonsmooth Analysis and Applications.

Adaptive Rigidity-Based Formation Control for Multirobotic Vehicles With Dynamics

In this brief, we introduce a graph rigidity-based, adaptive formation control law for multiple robotic vehicles moving on the plane that explicitly accounts for the vehicle dynamics while allowing for parametric uncertainty. We consider a class of vehicles modeled by Euler-Lagrange-like equations of motion. The control is designed via backstepping, and exploits rigid graph theory and the structural properties of the system dynamics. A Lyapunov analysis shows that the desired formation is acquired asymptotically. A five-vehicle simulation is used to illustrate the proposed formation acquisition control.

Further results on strict Lyapunov functions for rapidly time-varying nonlinear systems

We explicitly construct Lyapunov functions for rapidly time-varying nonlinear systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting dynamics which we assume are globally asymptotically stable. This leads to new sufficient conditions for global exponential, global asymptotic, and input-to-state stability of fast time-varying dynamics. We apply our results to two examples

A partial state feedback controller for trajectory tracking of rigid-link flexible-joint robots using an observed backstepping approach

This paper presents a partial state feedback controller for a rigid-link flexible joint (RLFJ) robot using an observed integrator backstepping approach. The robot controller requires only link position and actuator position measurements, and eliminates the need for measuring link velocity and actuator velocity. The controller uses two exact knowledge, second-order nonlinear observers to estimate the link and actuator velocities. The overall control system achieves a semiglobal exponential stability result for the link position and velocity tracking errors as well as the velocity observation errors. Stability proof and simulation results of the proposed partial state feedback controller are included in the paper.

Multi-agent formation maintenance and target tracking

In this paper, we introduce distance-based control laws for the multi-agent formation maintenance and target tracking problems. Using a single-integrator agent model, the proposed controls consist of a formation acquisition term, dependent on the potential function and graph rigidity matrix, and a formation maintenance or target tracking term. The control laws are only a function of the relative position of agents in an infinitesimally and minimally rigid graph, and either the desired velocity of the formation or the targets relative position to the leader and absolute velocity. A Lyapunov analysis shows that the origin of the distance error dynamics is locally exponentially stable, and, as a consequence, formation maintenance or target tracking can be readily proven.

A New Analytic Approximation for the Hydrodynamic Forces in Finite-Length Journal Bearings

A new method for determining a closed form expression for the hydrodynamic forces in finite-length plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely long (IL) or infinitely short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. A comparative computational study is presented for the steady-state behavior of the bearing system under static and unbalance loads. The results show the proposed models outperforming the standard limiting approximations as well as a model based on the finite-length impedance method.

Behavior of the ATP grasp domain of biotin carboxylase monomers and dimers studied using molecular dynamics simulations

The enzyme biotin carboxylase (BC) uses adenosine triphosphate (ATP) to carboxylate biotin and is involved in fatty acid synthesis. Structural evidence suggests that the B domain of BC undergoes a large hinge motion of ∼45° when binding and releasing substrates. Escherichia coli BC can function as a natural homodimer and as a mutant monomer. Using molecular dynamics simulations, we evaluate the free energy profile along a closure angle of the B domain of E. coli BC for three cases: a monomer without bound Mg2ATP, a monomer with bound Mg2ATP, and a homodimer with bound Mg2ATP in one subunit. The simulation results show that a closed state is the most probable for the monomer with or without bound Mg2ATP. For the dimer with Mg2ATP in one of its subunits, communication between the two subunits was observed. Specifically, in the dimer, the opening of the subunit without Mg2ATP caused the other subunit to open, and hysteresis was observed upon reclosing it. The most stable state of the dimer is one in which the B domain of both subunits is closed; however, the open state for the B domain without Mg2ATP is only approximately 2kBT higher in free energy than the closed state. A simple diffusion model indicates that the mean times for opening and closing of the B domain in the monomer with and without Mg2ATP are much smaller than the overall reaction time, which is on the order of seconds. Proteins 2011.

A new tracking controller for neuromuscular electrical stimulation under input delays: Case study in prediction

We announce a new tracking controller for neuromuscular electrical stimulation, which is an emerging technology that artificially stimulates skeletal muscles to help restore functionality to human limbs. The novelty of our work is that we prove that the tracking error globally asymptotically and locally exponentially converges to zero for any positive input delay, coupled with our ability to satisfy a state constraint imposed by the physical system. Also, our controller only requires sampled measurements of the states instead of continuous measurements, and allows perturbed sampling schedules, which can be important for practical purposes. Our work is based on a new method for constructing predictor maps for a large class of time-varying systems, which is of independent interest.

On the Stabilization of Planar Multi-Agent Formations

This paper is concerned with the decentralized formation control of multi-agent systems moving in the plane. Using a single-integrator agent model, we propose a new distributed control law to asymptotically stabilize the inter-agent distance error dynamics. Our approach exploits the infinitesimal and minimal rigidity of the undirected graph that models the formation. A Lyapunov-based analysis shows that these two properties are necessary conditions for asymtptotic stability. The control, which is explicitly dependent on the graph rigidity matrix, is derived for a class of potential functions.Copyright