Distance + Angle-Based Control of 2-D Rigid Formations.

A well-known problem with distance-based formation control is the existence of multiple equilibrium points not associated with the desired formation. This problem can be potentially mitigated by introducing an additional controlled variable. In this article, we generalize the distance + angle-based scheme for 2-D formations of single-integrator agents by using directed graphs and triangulation of the n-agent formation. We show that under certain conditions on the control gains and desired formation shape, our controller ensures the asymptotic stability of the correct formation for almost all initial agent positions.

Finite-Time Rigidity-Based Formation Maneuvering of Multiagent Systems Using Distributed Finite-Time Velocity Estimators.

In this paper, finite time rigidity-based formation maneuvering control of single integrator multiagent systems is considered. The target formation graph is assumed to be minimally and infinitesimally rigid, and the desired group velocity is considered to be available only to a subset of the agents. A distributed nonsmooth velocity estimator is used for each agent to estimate the desired group velocity in finite time. Using Lyapunov and input to state stability notions, a finite time distance-based formation maneuvering controller is presented and it is proved that by using the controller, agents converge to the target formation and track the desired group velocity in finite time. Furthermore, it is demonstrated that the designed controller is implementable in local coordinate frames of the agents. Simulation results are provided to show the effectiveness of the proposed control scheme.

Effects of exoskeleton use on movement kinematics during performance of common work tasks: A case study.

BACKGROUND: An exoskeleton may assist performance of basic work-related tasks. Its application should not alter user kinematics, which compromise user safety. OBJECTIVE: This case study was used to assess whether people wearing a lower-body K-SRDTM exoskeleton could complete common work tasks without altering kinematics that may increase injury risk. METHODS: Three males performed three tasks: kneeling and standing (kneel), lifting and lowering a weighted box floor-to-waist (lift), and stair-climbing with a weighted box (climb), all repeated with and without exoskeleton use (EXO, NONE). RESULTS: Kinematics with EXO often mimicked NONE. Hip and knee flexion with EXO often exceeded NONE without increasing heart rate for kneel. During lift with EXO, participants avoided greater lateral trunk flexion associated with injuries and used the preferred semi-squat technique. Participants produced more foot clearance with EXO than NONE during climb. Other outcomes of heart rate, perceived exertion, fatigue, and usability were mixed. CONCLUSIONS: EXO augmentation does not need to alter movement kinematics during performances of kneel, lift, and climb tasks. EXO kinematic alterations did not appear to compromise user safety in terms of lateral trunk bending. It may encourage good technique, such as greater foot clearance to avoid tripping, for some tasks, and changes in lifting strategies to avoid extreme flexion and protect passive tissues.

Rigidity-Based Multiagent Layered Formation Control.

This paper provides a solution to the nonplanar multiagent formation control problem using graph rigidity. We consider a 3-D multiagent formation control where multiple agents are operating in one plane and some other agents are operating outside of that plane. This can be referred to as a layered formation control where the objective is for all agents to cooperatively acquire a predefined formation shape using a decentralized control law. The proposed control strategy is based on regulating the interagent distances. A rigorous stability analysis is presented that guarantees convergence of these distances to desired values. Simulation results are presented to support the theoretical results.

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 Mg(2)ATP, a monomer with bound Mg(2)ATP, and a homodimer with bound Mg(2)ATP in one subunit. The simulation results show that a closed state is the most probable for the monomer with or without bound Mg(2)ATP. For the dimer with Mg(2)ATP in one of its subunits, communication between the two subunits was observed. Specifically, in the dimer, the opening of the subunit without Mg(2)ATP 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 Mg(2)ATP is only approximately 2k(B)T 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 Mg(2)ATP are much smaller than the overall reaction time, which is on the order of seconds.

Umbrella sampling simulations of biotin carboxylase: is a structure with an open ATP grasp domain stable in solution?

Biotin carboxylase is a homodimer that utilizes ATP to carboxylate biotin. Studies of the enzyme using X-ray crystallography revealed a prominent conformational change upon binding ATP. To determine the importance of this closing motion, the potential of mean force with the closure angle as a reaction coordinate was calculated using molecular dynamics simulations and umbrella sampling for a monomer of Escherichia coli biotin carboxylase in water with restraints to simulate attachment to a surface. The result suggests that the most stable state for the enzyme is a closed state different from both the ATP-bound and open state X-ray crystallography structures. There is also a significant motion of a region near the dimer interface not predicted by considering only open and closed configurations, which may have implications for the dynamics and activity of the dimer.

Modeling and numerical simulation of biotin carboxylase kinetics: implications for half-sites reactivity.

Biotin carboxylase catalyzes the ATP-dependent carboxylation of biotin and is one component of the multienzyme complex acetyl-CoA carboxylase that catalyzes the first committed step in fatty acid synthesis in all organisms. In Escherichia coli, biotin carboxylase exists as a homodimer where each subunit contains a complete active site. In a previous study (Janiyani, K., Bordelon, T., Waldrop, G.L., Cronan Jr., J.E., 2001. J. Biol. Chem. 276, 29864-29870), hybrid dimers were constructed where one subunit was wild-type and the other contained an active site mutation that reduced activity at least 100-fold. The activity of the hybrid dimers was only slightly greater than the activity of the mutant homodimers and far less than the expected 50% activity for completely independent active sites. Thus, there is communication between the two subunits of biotin carboxylase. The dominant negative effect of the mutations on the wild-type active site was interpreted as alternating catalytic cycles of the active sites in the homodimer. In order to test the hypothesis of oscillating catalytic cycles, mathematical modeling and numerical simulations of the kinetics of wild-type, hybrid dimers, and mutant homodimers of biotin carboxylase were performed. Numerical simulations of biotin carboxylase kinetics were the most similar to the experimental data when an oscillating active site model was used. In contrast, alternative models where the active sites were independent did not agree with the experimental data. Thus, the numerical simulations of the proposed kinetic model support the hypothesis that the two active sites of biotin carboxylase alternate their catalytic cycles.