791 research outputs found
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
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Robust hybrid global asymptotic stabilization of rigid body dynamics using dual quaternions
A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme
Application of Dual Quaternions to the problem of trajectory tracking with quadrotor-gimbal platform
We address the problem of state feedback trajectory tracking of the composite quadrotor-gimbal platform using the dual quaternion framework by extending the previuous result in [1] to the composite case. More precisely; we model the composite system using dual quaternion coordinates and derive the error dynamics which by inserting a PD + based control law has equilibrium points that is shown to be uniformly practical asymptoticly stable (UPAS)
Global Exponential Attitude Tracking Controls on SO(3)
This paper presents four types of tracking control systems for the attitude
dynamics of a rigid body. First, a smooth control system is constructed to
track a given desired attitude trajectory, while guaranteeing almost
semi-global exponential stability. It is extended to achieve global exponential
stability by using a hybrid control scheme based on multiple configuration
error functions. They are further extended to obtain robustness with respect to
a fixed disturbance using an integral term. The resulting robust, global
exponential stability for attitude tracking is the unique contribution of this
paper, and these are developed directly on the special orthogonal group to
avoid singularities of local coordinates, or ambiguities associated with
quaternions. The desirable features are illustrated by numerical examples
Koopman Operator Based Modeling and Control of Rigid Body Motion Represented by Dual Quaternions
In this paper, we systematically derive a finite set of Koopman based
observables to construct a lifted linear state space model that describes the
rigid body dynamics based on the dual quaternion representation. In general,
the Koopman operator is a linear infinite dimensional operator, which means
that the derived linear state space model of the rigid body dynamics will be
infinite-dimensional, which is not suitable for modeling and control design
purposes. Recently, finite approximations of the operator computed by means of
methods like the Extended Dynamic Mode Decomposition (EDMD) have shown
promising results for different classes of problems. However, without using an
appropriate set of observables in the EDMD approach, there can be no guarantees
that the computed approximation of the nonlinear dynamics is sufficiently
accurate. The major challenge in using the Koopman operator for constructing a
linear state space model is the choice of observables. State-of-the-art methods
in the field compute the approximations of the observables by using neural
networks, standard radial basis functions (RBFs), polynomials or heuristic
approximations of these functions. However, these observables might not
providea sufficiently accurate approximation or representation of the dynamics.
In contrast, we first show the pointwise convergence of the derived observable
functions to zero, thereby allowing us to choose a finite set of these
observables. Next, we use the derived observables in EDMD to compute the lifted
linear state and input matrices for the rigid body dynamics. Finally, we show
that an LQR type (linear) controller, which is designed based on the truncated
linear state space model, can steer the rigid body to a desired state while its
performance is commensurate with that of a nonlinear controller. The efficacy
of our approach is demonstrated through numerical simulations
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