A flow disturbance estimation and rejection strategy for multirotors with round-trip trajectories

This paper presents a round-trip strategy of multirotors subject to unknown flow disturbances. During the outbound flight, the vehicle immediately utilizes the wind disturbance estimations in feedback control, as an attempt to reduce the tracking error. During this phase, the disturbance estimations with respect to the position are also recorded for future use. For the return flight, the disturbances previously collected are then routed through a feedforward controller. The major assumption here is that the disturbances may vary over space, but not over time during the same mission. We demonstrate the effectiveness of this feedforward strategy via experiments with two different types of wind flows; a simple jet flow and a more complex flow. To use as a baseline case, a cascaded PD controller with an additional feedback loop for disturbance estimation was employed for outbound flights. To display our contributions regarding the additional feedforward approach, an additional feedforward correction term obtained via prerecorded data was integrated for the return flight. Compared to the baseline controller, the feedforward controller was observed to produce 43% less RMSE position error at a vehicle ground velocity of 1 m/s with 6 m/s of environmental wind velocity. This feedforward approach also produced 14% less RMSE position error for the complex flows as well

Stability Analysis of a Rigid Body with Attached Geometrically Nonlinear Rod by the Energy-Momentum Method

This paper applies the energy-momentum method to the problem of nonlinear stability of relative equilibria of a rigid body with attached flexible appendage in a uniformly rotating state. The appendage is modeled as a geometrically exact rod which allows for finite bending, shearing and twist in three dimensions. Application of the energy-momentum method to this example depends crucially on a special choice of variables in terms of which the second variation block diagonalizes into blocks associated with rigid body modes and internal vibration modes respectively. The analysis yields a nonlinear stability result which states that relative equilibria are nonlinearly stable provided that; (i) the angular velocity is bounded above by the square root of the minimum eigenvalue of an associated linear operator and, (ii) the whole assemblage is rotating about the minimum axis of inertia

A Quantitative and Standardized Robotic Method for the Evaluation of Arm Proprioception After Stroke

Stroke often results in both motor and sensory deficits, which may interact in the manifested functional impairment. Proprioception is known to play important roles in the planning and control of limb posture and movement; however, the impact of proprioceptive deficits on motor function has been difficult to elucidate due in part to the qualitative nature of available clinical tests. We present a quantitative and standardized method for evaluating proprioception in tasks directly relevant to those used to assess motor function. Using a robotic manipulandum that exerted controlled displacements of the hand, stroke participants were evaluated, and compared with a control group, in their ability to detect such displacements in a 2-alternative, forced-choice paradigm. A psychometric function parameterized the decision process underlying the detection of the hand displacements. The shape of this function was determined by a signal detection threshold and by the variability of the response about this threshold. Our automatic procedure differentiates between participants with and without proprioceptive deficits and quantifies functional proprioceptive sensation on a magnitude scale that is meaningful for ongoing studies of degraded motor function in comparable horizontal movements

A Robotic Test of Proprioception within the Hemiparetic Arm Post-stroke

Background: Proprioception plays important roles in planning and control of limb posture and movement. The impact of proprioceptive deficits on motor function post-stroke has been difficult to elucidate due to limitations in current tests of arm proprioception. Common clinical tests only provide ordinal assessment of proprioceptive integrity (eg. intact, impaired or absent). We introduce a standardized, quantitative method for evaluating proprioception within the arm on a continuous, ratio scale. We demonstrate the approach, which is based on signal detection theory of sensory psychophysics, in two tasks used to characterize motor function after stroke. Methods: Hemiparetic stroke survivors and neurologically intact participants attempted to detect displacement- or force-perturbations robotically applied to their arm in a two-interval, two-alternative forced-choice test. A logistic psychometric function parameterized detection of limb perturbations. The shape of this function is determined by two parameters: one corresponds to a signal detection threshold and the other to variability of responses about that threshold. These two parameters define a space in which proprioceptive sensation post-stroke can be compared to that of neurologically-intact people. We used an auditory tone discrimination task to control for potential comprehension, attention and memory deficits. Results: All but one stroke survivor demonstrated competence in performing two-alternative discrimination in the auditory training test. For the remaining stroke survivors, those with clinically identified proprioceptive deficits in the hemiparetic arm or hand had higher detection thresholds and exhibited greater response variability than individuals without proprioceptive deficits. We then identified a normative parameter space determined by the threshold and response variability data collected from neurologically intact participants. By plotting displacement detection performance within this normative space, stroke survivors with and without intact proprioception could be discriminated on a continuous scale that was sensitive to small performance variations, e.g. practice effects across days. Conclusions: The proposed method uses robotic perturbations similar to those used in ongoing studies of motor function post-stroke. The approach is sensitive to small changes in the proprioceptive detection of hand motions. We expect this new robotic assessment will empower future studies to characterize how proprioceptive deficits compromise limb posture and movement control in stroke survivors

Inter-Joint Coordination Deficits Revealed in the Decomposition of Endpoint Jerk During Goal-Directed Arm Movement After Stroke

It is well documented that neurological deficits after stroke can disrupt motor control processes that affect the smoothness of reaching movements. The smoothness of hand trajectories during multi-joint reaching depends on shoulder and elbow joint angular velocities and their successive derivatives as well as on the instantaneous arm configuration and its rate of change. Right-handed survivors of unilateral hemiparetic stroke and neurologically-intact control participants held the handle of a two-joint robot and made horizontal planar reaching movements. We decomposed endpoint jerk into components related to shoulder and elbow joint angular velocity, acceleration, and jerk. We observed an abnormal decomposition pattern in the most severely impaired stroke survivors consistent with deficits of inter-joint coordination. We then used numerical simulations of reaching movements to test whether the specific pattern of inter-joint coordination deficits observed experimentally could be explained by either a general increase in motor noise related to weakness or by an impaired ability to compensate for multi-joint interaction torque. Simulation results suggest that observed deficits in movement smoothness after stroke more likely reflect an impaired ability to compensate for multi-joint interaction torques rather than the mere presence of elevated motor noise

Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

Designing displaced lunar orbits using low-thrust propulsion

The design of spacecraft trajectories is a crucial task in space mission design. Solar sail technology appears as a promising form of advanced spacecraft propulsion which can enable exciting new space science mission concepts such as solar system exploration and deep space observation. Although solar sailing has been considered as a practical means of spacecraft propulsion only relatively recently, the fundamental ideas are by no means new (see McInnes1 for a detailed description). A solar sail is propelled by re ecting solar photons and therefore can transform the momentum of the photons into a propulsive force. This article focuses on designing displaced lunar orbits using low-thrust propulsion

A block diagonalization theorem in the energy-momentum method

We prove a geometric generalization of a block diagonalization theorem first found by the authors for rotating elastic rods. The result here is given in the general context of simple mechanical systems with a symmetry group acting by isometries on a configuration manifold. The result provides a choice of variables for linearized dynamics at a relative equilibrium which block diagonalizes the second variation of an augmented energy these variables effectively separate the rotational and internal vibrational modes. The second variation of the effective Hamiltonian is block diagonal. separating the modes completely. while the symplectic form has an off diagonal term which represents the dynamic interaction between these modes. Otherwise, the symplectic form is in a type of normal form. The result sets the stage for the development of useful criteria for bifurcation as well as the stability criteria found here. In addition, the techniques should apply to other systems as well, such as rotating fluid masses

The Dynamics of Ventilated Partial Cavities over a Wide Range of Reynolds Numbers and Quantitative 2D X-ray Densitometry for Multiphase Flow.

Ventilated partial cavity drag reduction is a technique that could potentially enable reduction of a ship's frictional drag, leading to a 5 to 20% net fuel savings, and thus providing economic and environmental benefits. Ventilated partial cavity drag reduction experiments were conducted using two geometrically similar experimental setups. First, experiments were performed at the world's largest re-circulating water channel, the U.S. Navy's Large Cavitation Channel (LCC), at Reynolds numbers to 80 million. For these experiments the LCC was adapted to allow free surface testing, which in itself was a major effort. The effect of the cavity closure geometry, and the cavity's robustness in the presence of global flow perturbations mimicking the effect of ambient waves were studied. Next, the experiments were reproduced at 1:14th size scale at Reynolds numbers of the order of one million, and in these small scale experiments the effect of Weber number was also investigated by reducing the surface tension by a factor of two. Results from these two sets of experiments were compared, and a potential scaling of required ventilation gas flux discussed. In addition the energy economics of the partial cavity drag reduction technique were analyzed. We can note that for partial cavities, the air entrainment is dominated by the cavity closure dynamics. To gain a better understanding of these dynamics, knowing the void fraction distribution, both spatially and temporally, would be very useful. In the cavity's closure region, as well as in most cavitating flows, any intrusive probe would perturb the flow greatly. X-ray densitometry offers a way to obtain a two dimensional time-resolved projection of the void fraction distribution, and a quantitative measure of the void fraction along the beam paths. An x-ray densitometry system was developed for use with a pre-existing cavitation tunnel. The limitations of the x-ray system were investigated, methods to contend with the imaging artifacts found, and the measured void fraction profiles compared against those obtained employing dual fiber optical probes and high speed video.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91443/1/smakihar_1.pd

Submovements During Reaching Movements after Stroke

Neurological deficits after cerebrovascular accidents very frequently disrupt the kinematics of voluntary movements with the consequent impact in daily life activities. Robotic methodologies enable the quantitative characterization of specific control deficits needed to understand the basis of functional impairments and to design effective rehabilitation therapies. In a group of right handed chronic stroke survivors (SS) with right side hemiparesis, intact proprioception, and differing levels of motor impairment, we used a robotic manipulandum to study right arm function during discrete point-to-point reaching movements and reciprocal out-and-back movements to visual targets. We compared these movements with those of neurologically intact individuals (NI). We analyzed the presence of secondary submovements in the initial (i.e. outward) trajectory portion of the two tasks and found that the SS with severe impairment (F