Constrained attitude maneuvers on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e116" altimg="si4.svg"><mml:mrow><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>: Rotation space sampling, planning and low-level control

Tan, Xiao; Berkane, Soulaimane; Dimarogonas, Dimos V.

doi:10.1016/j.automatica.2019.108659

Cited by 19 publications

(16 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One group uses path planning methods to search for a path from the initial attitude to the final attitude avoiding the keep-out cones. Path planning is performed by first operating a discretization, and then by searching for a feasible path by employing either a graph search algorithm [14,33,34] or a random search method [11]. Both search methods can become computationally demanding.…”

Section: Introductionmentioning

confidence: 99%

“…However, using those methods makes the attitude representation quite complex. In some works, including this one, attitude is represented on the special orthogonal group SO(3) [2,9,11,15,16,31,33] which is a global, unique, nonsingular, but nonminimal parametrization. However, nonminimality does not represent an issue when open-loop control torques are designed as in the present research.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

Celani

Bruni

2021

J Optim Theory Appl

View full text Add to dashboard Cite

This work presents an approach to spacecraft attitude motion planning which guarantees rest-to-rest maneuvers while satisfying pointing constraints. Attitude is represented on the group of three dimensional rotations. The angular velocity is expressed as weighted sum of some basis functions, and the weights are obtained by solving a constrained minimization problem in which the objective is the maneuvering time. However, the analytic expressions of objective and constraints of this minimization problem are not available. To solve the problem despite this obstacle, we propose to use a derivative-free approach based on sequential penalty. Moreover, to avoid local minima traps during the search, we propose to alternate phases in which two different objective functions are pursued. The control torque derived from the spacecraft inverse dynamics is continuously differentiable and vanishes at its endpoints. Results on practical cases taken from the literature demonstrate advantages over existing approaches.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

Celani

Bruni

2021

J Optim Theory Appl

View full text Add to dashboard Cite

show abstract

“…In addition, it features global attitude definition and one-to-one mapping [2]. SO(3) was utilized by Lee [3], Berkane et al [10], Akhtar et al [16], and Tan et al [18] to design their attitude controllers, and among them Berkane et al [10] relied only on attitude information using an angular velocity observer while Tan et al [18] employed an overlapping cell-like sampling on SO (3) to build a graph model on which a search algorithm was constructed to generate a feasible path. As opposed to SO(3), the Special Euclidean space SE(3) was used in Nikhilraj et al [14] to represent the attitude and an energy-optimal trajectory generation scheme was presented to drive the quadrotor to the desired state.…”

Section: Introductionmentioning

confidence: 99%

A Unified SO(3) Approach to the Attitude Control Design for Quadrotors

2021

IEEE Access

View full text Add to dashboard Cite

This paper proposes a two-phased problem reformulation approach to solve the quadrotor UAV attitude control problem. Given an initial attitude, the objective is to design a control to drive it toward a desired value. The first phase begins with the definition of three types of errors pertaining to attitude discrepancy, followed by the utilization of virtual control with which the dynamics of quadrotor's attitude and angular velocity are then unified under the framework of SO(3), rendering the original control problem much more transparent to tackle. Through cancellation of certain unwanted terms emerging from the unification process, entry-wise treatment of the remaining matrix dynamics is then employed in the second phase to transform it further into the stabilization problem of a 3-dimensional linear time-invariant system that is fairly easy to solve since to which standard feedback designs such as linear quadratic regulator and pole placement are readily applicable. In addition to the classical designs, a specialized and structurally simple controller is provided to reduce the number of gains. To account for system parametric uncertainties external disturbances, and sensor measurement errors and noises, a second controller based on classical H∞ theory is presented to enhance the robustness of the design. A numerical example is given, and computer simulations are conducted to generate error and control trajectories to assess and compare the effectiveness of the presented designs.

show abstract

“…For example, the attitude maneuvering of a space telescope observing galaxies requires to actively avoid the direct exposure to sun [7]. The constrained attitude problem is generally solved by considering the full attitude model (i.e., rotational space SO(3), quaternion representation, etc) [8]- [10]. However, in an under-actuated scenario, solutions for a full attitude is not applicable to a reduced attitude model.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we consider the constrained control problem on the 2−sphere within the framework of partitioning, planning and control modules [10]. More specifically, we propose a spherical polytope decomposition of the feasible region and develop control laws over these spherical polytopes.…”

Section: Introductionmentioning

confidence: 99%

Smooth Feedback Construction Over Spherical Polytopes

Tan

Berkane

Dimarogonas

2020

2020 European Control Conference (ECC)

Self Cite

View full text Add to dashboard Cite

In this work, we investigate the partitioning and control problems on the 2−sphere, the set of all unit vectors in R 3. Specifically, we present a spherical-polytope-based partitioning for the 2−sphere and then propose a novel approach to construct a feedback control law over a given set of spherical polytopes. Instead of designing the control law directly on the sphere, we propose a smooth atlas on it based on the gnomonic projection. We further show that the gnomonic map projects the spherical polytopes to Euclidean polytopes. Moreover, the kinematics evolving on a spherical polytope can be transformed via feedback into a single integrator in the Euclidean space. Thanks to these properties, control algorithms that were originally developed for polytopes in Euclidean spaces can now be applied to spherical polytopes on the 2−sphere. We conclude this paper by showing a control construction on the sphere with cluttered obstacles.

show abstract

Constrained attitude maneuvers on SO(3): Rotation space sampling, planning and low-level control

Cited by 19 publications

References 15 publications

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

A Unified SO(3) Approach to the Attitude Control Design for Quadrotors

Smooth Feedback Construction Over Spherical Polytopes

Contact Info

Product

Resources

About