1,721,058 research outputs found
An inverse dynamics approach to the guidance of spacecraft in close proximity of tumbling debris
No full textThis paper proposes a trajectory planning method based on polynomial shaping, applied to the docking scenario in the framework of an Active Debris Removal mission. A tumbling, uncooperative target with an asymmetric inertia tensor is considered. Closed-form solutions of the target's motion are obtained from an approximated axisymmetric model, which are incorporated to the trajectory planning algorithm. The close approach and docking strategy is designed in three different segments, in order to enhance the safety of the manoeuvre. Fuel is optimised amongst the class of polynomial trajectories considered, and thrust constraints are taken into account via inverse dynamics. The trajectory planning algorithm is implemented in a closed-loop guidance scheme, which simulations show to be robust to large sensor sample times and external disturbances
Integrating Hamiltonian systems defined on the Lie groups SO(4) and SO(1,3)
No full textIn this paper we study constrained optimal control problems on semi-simple Lie groups. These constrained optimal control problems include Riemannian, sub-Riemannian, elastic and mechanical problems. We begin by lifting these problems, through the Maximum Principle, to their associated Hamiltonian formalism. As the base manifold is a Lie group G the cotangent bundle is realized as the direct product G×g∗ where g∗ is the dual of the Lie algebra g of G. The solutions to these Hamiltonian vector fields l Eg∗, are called extremal curves and the projections g(t) E G are the corresponding optimal solutions. The main contribution of this paper is a method for deriving explicit expressions relating the extremal curves l E g∗ to the optimal solutions g(t) E G for the special cases of the Lie groups SO(4) and SO(1,3). This method uses the double cover property of these Lie groups to decouple them into lower dimensional systems. These lower dimensional systems are then solved in terms of the extremals using a coordinate representation and the systems dynamic constraints. This illustrates that the optimal solutions g(t) E G are explicitly dependent on the extremal curves
A motion planning method for spacecraft attitude maneuvers using single polynomials
No full textA motion planning technique for generating smooth attitude slew maneuvers is presented, which can generate suboptimal feasible trajectories with low computational cost in the presence of constraints. The attitude coordinates are shaped by time-dependent polynomials, whose coefficients are determined by matching prescribed arbitrary boundary conditions. Quaternions are used as the reference attitude parametrization for arbitrary maneuvers, which require normalization of the four independently shaped coordinates. In the case of spin-to-spin maneuvers, a particular combination of Euler Angles are used. The torque profile is evaluated using inverse dynamics, which allows the feasibility of the maneuver given the actuator constraints to be checked. With this approach, a root-finding method is used to select the minimum time for a certain path. By increasing the degree of the polynomial free coefficients are introduced, thus pointing constraints can be accommodated and time can be optimized amongst this class of motion. This motion planning method is applied to a flexible spacecraft model, demonstrating its effectiveness at reducing spillover vibrations
Geometric attitude motion planning for spacecraft with pointing and actuator constraints
Full text linkThis article presents a semianalytical method for motion planning with pointing and dynamic constraints in two stages where the path-planning problem with pointing constraints is addressed using parameter optimization of an analytically defined cost function on the virtual domain and dynamic constraints are addressed on the real time domain. The analytical formulation of the problem allows a simple method for reshaping the path between two prescribed rotations so that it can avoid forbidden regions. The approach described in this article has the advantage that it is simple to implement, deterministic, does not require discretization or integration, is easily adjusted to satisfy actuator constraints, and is expressed explicitly on the special orthogonal group SO(3)
A quaternion-based attitude tracking controller for robotic systems
Full text linkThis paper presents a new quaternion-based attitude tracking controller. A general Lyapunov function is defined whose derivative is control dependent and a control is chosen to guarantee asymptotic stability of the zero-error state. The corresponding closed loop error dynamics are shown to reduce to a simple 1 degree of freedom description in terms of the eigen-axis angle error. The main contribution of this paper is to present a special case where the closed-loop error dynamics reduce to a simple linear oscillator description (without the need for linearisation). This means that the controller can be tuned to guarantee exponentially fast tracking with a damped response and without oscillation
Analytical perturbation method for frozen orbits around the asteroid 433 Eros
No full textIn this paper a method for obtaining initial condition for frozen orbits around fast rotating, highly irregular bodies is presented. Such method is based on a general perturbative theory of motion, for inhomogeneous gravitational fields. Taking into account the terms of the gravitational potential up to an arbitrary order to construct a precise Hamiltonian formulation of the problem, the system is averaged both over the argument of node and the mean anomaly, to reduce its complexity (i.e. the number of degrees of freedom). An approximate system is obtained, which provides an accurate description of the dynamics of the initial system. This can be applied to every celestial body and in particular, can be exploited for constructing a method for finding initial conditions to yield frozen orbits. These orbits can then be used as reference trajectories in missions that require close inspection of asteroids. To this end applications to derive frozen orbits for Eros 433 have been provided which could be of key interest for every observational, discovery mission around this asteroid
Optimal geometric motion planning for a spin-stabilized spacecraft
No full textA method requiring low-computational overhead is presented which generates low-torque reference motions between arbitrary orientations for spin-stabilized spacecraft. The initial stage solves a constrained optimal control problem deriving analytical solutions for a class of smooth and feasible reference motions. Specifically, for a quadratic cost function an application of Pontryagin’s maximum principle leads to a completely integrable Hamiltonian system that is, exactly solvable in closed-form, expressed in terms of several free parameters. This is shown to reduce the complexity of a practical motion planning problem from a constrained functional optimization problem to an unconstrained parameter optimization problem. The generated reference motions are then tracked using an augmented quaternion feedback law, consisting of the sum of a proportional plus derivative term and a term to compensate nonlinear dynamics. The method is illustrated with an application to re-point a spin-stabilized agile micro-spacecraft using zero propellant. The low computational overhead of the method enhances its suitability for on-board motion generation
Nonlinearly stable equilibria in the Sun-Jupiter-Trojan-Spacecraft four body problem
No full textThe Trojan asteroids have been highlighted as a main target for future discovery missions, which will enable key questions about the formation of our Solar system to be answered. Programs like the Japanese Jupiter and Trojan Asteroids Exploration Programme are already testing technology demonstrators like the IKAROS spacecraft to enable future interplanetary missions to Jupiter and the Trojans. In this paper an analytic analysis of the stability of the Low thrust Sun Jupiter Asteroid Spacecraft system, is presented, from a Hamiltonian point of view. Setting the three primaries in the stable Lagrangian equilateral triangle configuration, eight natural (i.e. with zero thrust) equilibrium points are identified, four of which are close to the asteroid, two stable and two unstable, when considering as primaries the Sun and any other two bodies of the Solar System. Artificial equilibria, which can be seen as low thrust perturbations of the natural ones, are then taken into account with the aim of identifying their linearly stable subset. The Lyapunov stability of these marginally stable points is then analysed using basic KAM (Kolmogorov Arnold Moser) theory and Arnold’s stability theorem. In order to apply such theorem an iterative procedure to reduce the Hamiltonian into Birkhoff’s Normal Form is applied up to fourth order, explicitly defining, at each step, the generating function of a symplectic transformation. Despite the complexity of this process, Normal Forms are a fundamental, necessary step for any application of KAM theory; such theory, transforming a non-integrable system into a sum of perturbed integrable ones, enables the computation of a high order analytical approximation of the system dynamics, plus an estimation of the discrepancy from the initial model. As an application of KAM theory, a proof of the nonlinear stability for the low thrust generated equilibrium points under non resonant conditions is found using Arnold’s stability theorem. Results show that Lyapunov stability is guaranteed along the linearly stable domain with the exception of a set of points with zero measure where the conditions to apply Arnold‘s theorem are not satisfied
Low thrust propulsion in a coplanar circular restricted four body problem
No full textThis 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
Analytic perturbative theories in highly inhomogeneous gravitational fields
No full textOrbital motion about irregular bodies is highly nonlinear due to inhomogeneities in the gravitational field. Classical theories of motion close to spheroidal bodies cannot be applied as for inhomogeneous bodies the Keplerian forces do not provide a good approximation of the system dynamics. In this paper a closed form, analytical method for developing the motion of a spacecraft around small bodies is presented, for the so called fast rotating case, which generalize previous results to second order, arbitrary degree, gravitational fields. Through the application of two different Lie transformations, suitable changes of coordinates are found, which reduce the initial non integrable Hamiltonian of the system into an integrable one plus a negligible, perturbative remainder of higher degree. In addition, an explicit analytical formulation for the relegated, first and second order, arbitrary degree Hamiltonian for relatively high altitude motion in any inhomogeneous gravitational field is derived in closed-form. Applications of this algorithm include a method for determining initial conditions for frozen orbits around any irregular body by simply prescribing the desired inclination and eccentricity of the orbit. This method essentially reduces the problem of computing frozen orbits to a problem of solving a 2-D algebraic equation. Results are shown for the asteroid 433-Eros
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