Singularities of optimal attitude motions

This paper considers the problem of planning optimal attitude motions for spacecraft. The extremal solutions that result from this optimization problem are characterized and their singularities identified. Following this these singularities are solved analytically inferring the form of particular optimal velocities. These particular solutions are then integrated and their corresponding motions derived independently of a local coordinate chart. These motions have the potential to be used as smooth, optimal reference trajectories for performing certain re-orientations for spacecraft

Extension of low-thrust propulsion to the autonomous coplanar circular restricted four body problem with application to future Trojan Asteroid missions

An Autonomous Coplanar Circular Restricted Four Body Problem (CRFBP) is considered, where the massless body is a low-thrust spacecraft. 'Natural' and 'artificial' (i.e. created with the use of continuous low-thrust propulsion) equilibrium solutions are identified, that have the potential to be exploited in future science missions. Results show that, with zero thrust, there are unstable equilibrium points close to the third primary. However, artificial equilibrium points, displaced from the natural ones, can be generated with the use of constant low-thrust. Furthermore, these points are proved to be stable in certain regions about the third primary mass. This is particularly advantageous since it means that it would be possible to continuously maintain a spacecraft about these strategic observation points, close to the smaller primary, without the need for state feedback control. The Sun-Jupiter-Trojan Asteroid-Spacecraft system is considered, as a particular case of the Autonomous Coplanar CRFBP. Curves of artificial equilibrium points are then identified. Furthermore, the stability analysis of these points reveals the region where they are stable. In this region four bounded orbits close to the Asteroid are proved to exist, that can be reached and maintained with a constant low-thrust lower than 10µN

Stabilizing periodic orbits above the elliptic plane in the solar sail 3-body problem

We consider periodic orbits high above the ecliptic plane in the Elliptic Restricted Three-Body Problem where the third massless body is a solar sail. Periodic orbits above the ecliptic are of practical interest as they are ideally positioned for the year-round constant imaging of, and communication with, the poles. Initially we identify an unstable periodic orbit by using a numerical continuation from a known periodic orbit above the ecliptic in the circular case with the eccentricity as the varying parameter. This orbit is then used to construct a reference trajectory for the sail to track. In addition we illustrate an alternative method for constructing a periodic reference trajectory based on a time-delayed feedback mechanism. The reference trajectories are then tracked using a linear feedback regulator (LQR) where the control actuation is delivered by varying the solar sails orientation. Using this method it is shown that a 'near term' solar sail is capable of performing stable periodic motions high above the ecliptic

New periodic orbits in the solar sail restricted three body problem

In this paper we consider periodic orbits of a solar sail in the Earth-Sun restricted three-body problem. In particular, we consider orbits which are high above the ecliptic plane, in contrast to the classical Halo orbits about the collinear equilibria. We begin with the Circular Restricted Three-Body Problem (CRTBP) where periodic orbits about equilibria are naturally present at linear order. Using the method of Lindstedt-Poincaré, we construct nth order approximations to periodic solutions of the nonlinear equations of motion. In the second part of the paper we generalize to the Elliptic Restricted Three Body Problem (ERTBP). A numerical continuation, with the eccentricity, e, as the varying parameter, is used to find periodic orbits above the ecliptic, starting from a known orbit at e = 0 and continuing to the required eccentricity of e = 0:0167. The stability of these periodic orbits is investigated

Design of optimal transfers between North and South Pole-sitter orbits

Recent studies have shown the feasibility of an Earth pole-sitter mission, where a spacecraft follows the Earth’s polar axis to have a continuous, hemispherical view of one of the Earth’s Poles. However, due to the tilt of the polar axis, the North and South Poles are alternately situated in darkness for long periods dur-ing the year. This significantly constrains observations and decreases mission scientific return. This paper therefore investigates transfers between north and south pole-sitter orbits before the start of the Arctic and Antarctic winters to maximize scientific return by observing the polar regions only when lit. Clearly, such a transfer can also be employed for the sole purpose of visiting both the North and South Poles with one single spacecraft during one single mission. To enable such a novel transfer, two types of propulsion are proposed, including so-lar electric propulsion (SEP) and a hybridization of SEP with solar sailing. A di-rect optimization method based on pseudospectral transcription is used to find both transfers that minimize the SEP propellant consumption and transfers that trade-off SEP propellant consumption and observation time of the Poles. Also, a feedback control is developed to account for non-ideal properties of the solar sail. It is shown that, for all cases considered, hybrid low-thrust propulsion out-performs the pure SEP case, while enabling a transfer that would not be feasible with current solar sail technology

Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping

Low thrust propulsion in a coplanar circular restricted four body problem

This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model

Reaching across continents : engaging students through virtual collaborations

Business schools have the responsibility of preparing students for work in multicultural organizations and global markets. This paper examines a situated learning experience for undergraduates through a virtual collaboration between a UK university and a Brazilian university. This facilitated remote communication using social media and smart devices, allowing students from both institutions to enhance their cross-cultural management competencies. A qualitative approach was used for the research, drawing on the reflections of the tutors from both institutions, and feedback received from students in the UK and Brazil. This paper provides empirical observations regarding the use of this innovative pedagogic approach, generating discussion of the implications for teaching, thus contributing to the literature on international collaborations in cross-cultural management education