Path planning for simple wheeled robots : sub-Riemannian and elastic curves on SE(2)

This paper presents a motion planning method for a simple wheeled robot in two cases: (i) where translational and rotational speeds are arbitrary and (ii) where the robot is constrained to move forwards at unit speed. The motions are generated by formulating a constrained optimal control problem on the Special Euclidean group SE(2). An application of Pontryagin’s maximum principle for arbitrary speeds yields an optimal Hamiltonian which is completely integrable in terms of Jacobi elliptic functions. In the unit speed case, the rotational velocity is described in terms of elliptic integrals and the expression for the position reduced to quadratures. Reachable sets are defined in the arbitrary speed case and a numerical plot of the time-limited reachable sets presented for the unit speed case. The resulting analytical functions for the position and orientation of the robot can be parametrically optimised to match prescribed target states within the reachable sets. The method is shown to be easily adapted to obstacle avoidance for static obstacles in a known environment

The Health Consequences of Senior Hunger in the United States: Evidence from the 1999-2010 NHANES

Millions of seniors are food insecure in the United States, meaning that scores do not have access to enough food at all times for an active, healthy life. What makes food insecurity an even more pressing issue is its association with a wide array of negative nutrition and health consequences. In earlier reports on food insecurity among seniors it was documented that food insecure seniors, even after controlling for other factors, were at higher risk of experiencing negative nutrition and health consequences than food secure seniors. In this report, we build on those earlier findings in three main directions. Namely, we add in several new health outcomes; we use four more years of data ; and we examine how trends in health and nutrition outcomes among food secure and food insecure seniors have changed over the past decade. Using data from the 1999-2010 National Health and Nutrition Examination Survey (NHANES), we considered the following outcomes related to nutrient intakes: energy intake, protein, vitamin A, vitamin C, thiamin, riboflavin, vitamin B6, calcium, phosphorous, magnesium, and iron. The set of health outcomes we analyzed were diabetes, general health , depression, diabetes, ADL limitations, high blood pressure, high cholesterol, congestive heart failure, coronary heart disease, cancer, reports of chest pain, gum disease, psoriasis, asthma, having had a heart attack, and a self-report of gum health

Attitude motion planning for a spin stabilised disk sail

While solar sails are capable of providing continuous low thrust propulsion the size and flexibility of the sail structure poses difficulties to their attitude control. Rapid slewing of the sail can cause excitation of structural modes, resulting in flexing and oscillation of the sail film and a subsequent loss of performance and decrease in controllability. Disk shaped solar sails are particularly flexible as they have no supporting structure and so these spacecraft must be spun around their major axis to stiffen the sail membrane via the centrifugal force. In addition to stiffening the structure this spin stabilisation also provides gyroscopic stiffness to disturbances, aiding the spacecraft in maintaining its desired attitude. A method is applied which generates smooth reference motions between arbitrary orientations for a spin-stabilised disk sail. The method minimises the sum square of the body rates of the spacecraft, therefore ensuring that the generated attitude slews are slow and smooth, while the spin stabilisation provides gyroscopic stiffness to disturbances. An application of Pontryagin’s maximum principle yields an optimal Hamiltonian which is completely solvable in closed form. The resulting analytical expressions are a function of several free parameters enabling parametric optimisation to be used to provide reference motions which match prescribed boundary conditions on the initial and final configurations. The generated reference motions are utilised in the repointing of a 70m radius spin-stabilised disk solar sail in a heliocentric orbit, with the aim of assessing the feasibility of the motion planning method in terms of the control torques required to track the motions

Sequence-Based Mapping and Genome Editing Reveal Mutations in Stickleback Hps5 Cause Oculocutaneous Albinism and the casper Phenotype.

Here, we present and characterize the spontaneous X-linked recessive mutation casper, which causes oculocutaneous albinism in threespine sticklebacks (Gasterosteus aculeatus). In humans, Hermansky-Pudlak syndrome results in pigmentation defects due to disrupted formation of the melanin-containing lysosomal-related organelle (LRO), the melanosome. casper mutants display not only reduced pigmentation of melanosomes in melanophores, but also reductions in the iridescent silver color from iridophores, while the yellow pigmentation from xanthophores appears unaffected. We mapped casper using high-throughput sequencing of genomic DNA from bulked casper mutants to a region of the stickleback X chromosome (chromosome 19) near the stickleback ortholog of Hermansky-Pudlak syndrome 5 (Hps5). casper mutants have an insertion of a single nucleotide in the sixth exon of Hps5, predicted to generate an early frameshift. Genome editing using CRISPR/Cas9 induced lesions in Hps5 and phenocopied the casper mutation. Injecting single or paired Hps5 guide RNAs revealed higher incidences of genomic deletions from paired guide RNAs compared to single gRNAs. Stickleback Hps5 provides a genetic system where a hemizygous locus in XY males and a diploid locus in XX females can be used to generate an easily scored visible phenotype, facilitating quantitative studies of different genome editing approaches. Lastly, we show the ability to better visualize patterns of fluorescent transgenic reporters in Hps5 mutant fish. Thus, Hps5 mutations present an opportunity to study pigmented LROs in the emerging stickleback model system, as well as a tool to aid in assaying genome editing and visualizing enhancer activity in transgenic fish

A new approach to the solution of free rigid body motion for attitude manoeuvers

A Hamiltonian formulation of free rigid body motion defined on the Special Unitary Group SU(2) is used to integrate the system to obtain a convenient quaternion representation for attitude engineering applications. Novel content of this paper concerns applying a modern approach, based on geometric control theory to obtain the kinematic solution in an elegant and compact form. Moreover, this integration leads to an attitude representation which is not Euler-angle-like, thus enhancing its applicability (e.g. to attitude motion design)

Planning natural repointing manoeuvres for nano-spacecraft

In this paper the natural dynamics of a rigid body are exploited to plan attitude manoeuvres for a small spacecraft. By utilising the analytical solutions of the angular velocities and making use of Lax pair integration, the time evolution of the attitude of the spacecraft in a convenient quaternion form is derived. This enables repointing manoeuvres to be generated by optimising the free parameters of the analytical expressions, the initial angular velocities of the spacecraft, to match prescribed boundary conditions on the final attitude of the spacecraft. This produces reference motions which can be tracked using a simple proportional-derivative controller. The natural motions are compared in simulation to a conventional quaternion feedback controller and found to require lower accumulated torque. A simple obstacle avoidance algorithm, exploiting the analytic form of natural motions, is also described and implemented in simulation. The computational efficiency of the motion planning method is discussed

Planning natural repointing manoeuvres for nano-spacecraft

In this paper the natural dynamics of a rigid body are exploited to plan attitude manoeuvres for a small spacecraft. By utilising the analytical solutions of the angular velocities and making use of Lax pair integration, the time evolution of the attitude of the spacecraft in a convenient quaternion form is derived. This enables repointing manoeuvres to be generated by optimising the free parameters of the analytical expressions, the initial angular velocities of the spacecraft, to match prescribed boundary conditions on the final attitude of the spacecraft. This produces reference motions which can be tracked using a simple proportional-derivative controller. The natural motions are compared in simulation to a conventional quaternion feedback controller and found to require lower accumulated torque. A simple obstacle avoidance algorithm, exploiting the analytic form of natural motions, is also described and implemented in simulation. The computational efficiency of the motion planning method is discussed

Computationally light attitude controls for resource limited nano-spacecraft

Nano-spacecraft have emerged as practical alternatives to large conventional spacecraft for specific missions (e.g. as technology demonstrators) due to their low cost and short time to launch. However these spacecraft have a number of limitations compared to larger spacecraft: a tendency to tumble post-launch; lower computational power in relation to larger satellites and limited propulsion systems due to small payload capacity. As a result new methodologies for attitude control are required to meet the challenges associated with nano-spacecraft. This paper presents two novel attitude control methods to tackle two phases of a mission using zero-propellant (i) the detumbling post-launch and (ii) the repointing of nano-spacecraft. The first method consists of a time-delayed feedback control law which is applied to a magnetically actuated spacecraft and used for autonomous detumbling. The second uses geometric mechanics to construct zero propellant reference manoeuvres which are then tracked using quaternion feedback control. The problem of detumbling a magnetically actuated spacecraft in the first phase of a mission is conventionally tackled using BDOT control. This involves applying controls which are proportional to the rate of change of the magnetic field. However, real systems contain sensor noise which can lead to discontinuities in the signal and problems with computing the numerical derivative. This means that a noise filter must be used and this increases the computational overhead of the system. It is shown that a timedelayed feedback control law is advantageous as the use of a delayed signal rather than a derivative negates the need for such a filter, thus reducing computational overhead. The second phase of the mission is the repointing of the spacecraft to a desired target. Exploiting the analytic solutions of the angular velocities of a symmetric spacecraft and further using Lax pair integration it is possible to derive exact equations of the natural motions including the time evolution of the quaternions. It is shown that parametric optimisation of these solutions can be used to generate low torque reference motions that match prescribed boundary conditions on the initial and final configurations. Through numerical simulation it is shown that these references can be tracked using nanospacecraft reaction wheels while eigenaxis rotations, used for comparison, are more torque intensive. As the method requires parameter optimisation as opposed to optimisation methods that require numerical integration, the computational effort is reduced

Heteroclinic optimal control solutions for attitude motion planning

An analytical attitude motion planning method is presented that exploits the heteroclinic connections of an optimal kinematic control problem. This class of motion, of hyperbolic type, supply a special case of analytically defined rotations that can be further optimised to select a suitable reference motion that minimises accumulated torque and the final orientation error amongst these motions. This analytical approach could be used to improve the overall performance of a spacecraft’s attitude dynamics and control system when used alongside current flight tested tracking controllers. The resulting algorithm only involves optimising a small number of parameters of standard functions and is simple to implement