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

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

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

Limits to compensatory adaptation and the persistence of antibiotic resistance in pathogenic bacteria

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Program (FP7/2007-2013)/ERC grant agreement no. 281591 and from the Royal Society.Peer reviewedPublisher PD

Stochastic bacterial population dynamics restrict the establishment of antibiotic resistance from single cells

A better understanding of how antibiotic exposure impacts the evolution of resistance in bacterial populations is crucial for designing more sustainable treatment strategies. The conventional approach to this question is to measure the range of concentrations over which resistant strain(s) are selectively favored over a sensitive strain. Here, we instead investigate how antibiotic concentration impacts the initial establishment of resistance from single cells, mimicking the clonal expansion of a resistant lineage following mutation or horizontal gene transfer. Using two Pseudomonas aeruginosa strains carrying resistance plasmids, we show that single resistant cells have <5% probability of detectable outgrowth at antibiotic concentrations as low as one-eighth of the resistant strain’s minimum inhibitory concentration (MIC). This low probability of establishment is due to detrimental effects of antibiotics on resistant cells, coupled with the inherently stochastic nature of cell division and death on the single-cell level, which leads to loss of many nascent resistant lineages. Our findings suggest that moderate doses of antibiotics, well below the MIC of resistant strains, may effectively restrict de novo emergence of resistance even though they cannot clear already-large resistant populations

Positive allosteric modulators of the a-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor

L-glutamate is the major excitatory neurotransmitter in the mammalian central nervous system (CNS) and plays a fundamental role in the control of motor function, cognition and mood. The physiological effects of glutamate are mediated through two functionally distinct receptor families. While activation of metabotropic (G-protein coupled) glutamate receptors results in modulation of neuronal excitability and transmission, the ionotropic glutamate receptors (ligand-gated ion channels) are responsible for mediating the fast synaptic response to extracellular glutamate