Minimum Disturbance Attitude Control Algorithm for DFFSR

Aiming at the attitude disturbance problem of Dual-arm Free Flying Space Robot(DFFSR), firstly, the kinematics equation of DFFSR has been established by using the geometric relationship of each link of DFFSR, the characteristic equation of manipulator, and the linear momentum and angular momentum conservation law of the system in microgravity environment; Secondly, based on the established Generalized Jacobian Matrix(GJM) describing the relationship between the end-effector motion velocity of DFFSR manipulator and the motion velocity of each joint, the relationship between the motion velocity of each joint of DFFSR manipulator and the angular velocity of satellite base has been derived, and the attitude interference model of DFFSR has been established; Finally, the Minimum Attitude Disturbance Map(MADM) algorithm for calculating the DFFSR manipulator has been established, and the attitude control algorithm based on MADM has been proposed. The attitude control method can ensure that the attitude of the satellite base of DFFSR remains unchanged during the movement of the manipulator.

Intelligence-Aware Batch Processing for TMA with Bearings-Only Measurements

This paper develops a framework to track the trajectory of a target in 2D by considering a moving ownship able to measure bearing measurements. Notably, the framework allows one to incorporate additional information (e.g., obtained via intelligence) such as knowledge on the fact the target’s trajectory is contained in the intersection of some sets or the fact it lies outside the union of other sets. The approach is formally characterized by providing a constrained maximum likelihood estimation (MLE) formulation and by extending the definition of the Cramér–Rao lower bound (CRLB) matrix to the case of MLE problems with inequality constraints, relying on the concept of generalized Jacobian matrix. Moreover, based on the additional information, the ownship motion is chosen by mimicking the Artificial Potential Fields technique that is typically used by mobile robots to aim at a goal (in this case, the region where the target is assumed to be) while avoiding obstacles (i.e., the region that is assumed not to intersect the target’s trajectory). In order to show the effectiveness of the proposed approach, the paper is complemented by a simulation campaign where the MLE computations are carried out via an evolutionary ant colony optimization software, namely, mixed-integer distributed ant colony optimization solver (MIDACO-SOLVER). As a result, the proposed framework exhibits remarkably better performance, and in particular, we observe that the solution is less likely to remain stuck in unsatisfactory local minima during the MLE computation.

Aerial Manipulator Control Method Based on Generalized Jacobian

This paper describes a control method for an aerial manipulator on an unmanned aerial vehicle (UAV) by using a generalized Jacobian (GJ). Our task is to realize visual check of bridge inspection by employing a UAV with a multi-degree-of-freedom (DoF) manipulator on its top. The manipulator is controlled by using the GJ. Subsequently, by comparing the aerial manipulator control with a conventional Jacobian experimentally, we discovered that the accuracy of the control improved by applying the GJ. The manipulator has three DoFs in the X-Z plane of the UAV coordinate system. The experiment shows that the manipulator controlled with the GJ can compensate for the pose error of the body by 54.5% and 47.7% in the X- and Z-axes, respectively.

Jacobian Nonsingularity in Nonlinear Symmetric Conic Programming Problems and Its Application

This paper considers the nonlinear symmetric conic programming (NSCP) problems. Firstly, a type of strong sufficient optimality condition for NSCP problems in terms of a linear-quadratic term is introduced. Then, a sufficient condition of the nonsingularity of Clarke’s generalized Jacobian of the Karush–Kuhn–Tucker (KKT) system is demonstrated. At last, as an application, this property is used to obtain the local convergence properties of a sequential quadratic programming- (SQP-) type method.

Quantum Cohomology and Closed-String Mirror Symmetry for Toric Varieties

We give a short new computation of the quantum cohomology of an arbitrary smooth (semiprojective) toric variety $X$, by showing directly that the Kodaira–Spencer map of Fukaya–Oh–Ohta–Ono defines an isomorphism onto a suitable Jacobian ring. In contrast to previous results of this kind, $X$ need not be compact. The proof is based on the purely algebraic fact that a class of generalized Jacobian rings associated to $X$ are free as modules over the Novikov ring. When $X$ is monotone the presentation we obtain is completely explicit, using only well-known computations with the standard complex structure.

Trajectory Planning Based on Screw Theory with Consideration of the Optimal Berth Position for a Space Robot

Trajectory planning is a prerequisite for the tracking control of a free-floating space robot. There are usually multiple planning objectives, such as the pose of the end-effector and the base attitude. In efforts to achieve these goals, joint variables are often taken as exclusive operable parameters, while the berth position is neglected. This paper provides a novel trajectory planning strategy that considers the berth position by applying screw theory and an optimization method. First, kinematic equations at the position level are established on the basis of the product of exponential formula and the conservation of the linear momentum of the system. Then, generalized Jacobian matrices of the base and end-effector are derived separately. According to the differential relationship, an ordinary differential equation for the base attitude is established, and it is solved by the modified Euler method. With these sufficient and necessary preconditions, a parametric optimization strategy is proposed for two trajectory planning cases: zero attitude disturbance and attitude adjustment of the base. First, the berth position is transformed into the desired position of the end-effector, and its constraints are described. Joint variables are parameterized using a sinusoidal function combined with a five-order polynomial function. Then, objective functions are constructed. Finally, a genetic algorithm with a modified mutation operator is used to solve this optimization problem. The optimal berth position and optimized trajectory are obtained synchronously. The simulation of a planar dual-link space robot demonstrates that the proposed strategy is feasible, concise, and efficient.

Fourier–Mukai and autoduality for compactified Jacobians. I

To every singular reduced projective curve X one can associate, following Esteves, many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compactification of a disjoint union of the generalized Jacobian of X. We prove that, for a reduced curve with locally planar singularities, the integral (or Fourier–Mukai) transform with kernel the Poincaré sheaf from the derived category of the generalized Jacobian of X to the derived category of any fine compactified Jacobian of X is fully faithful, generalizing a previous result of Arinkin in the case of integral curves. As a consequence, we prove that there is a canonical isomorphism (called autoduality) between the generalized Jacobian of X and the connected component of the identity of the Picard scheme of any fine compactified Jacobian of X and that algebraic equivalence and numerical equivalence of line bundles coincide on any fine compactified Jacobian, generalizing previous results of Arinkin, Esteves, Gagné, Kleiman, Rocha, and Sawon.The paper contains an Appendix in which we explain how our work can be interpreted in view of the Langlands duality for the Higgs bundles as proposed by Donagi–Pantev.