Local and Multilocal Scale-Space Description

Subsurface media are in general anisotropic, and this fact should be taken into account for analyzing reflection and transmission (R/T) coefficients. Orthorhombic (ORT) media are commonly regarded as a practical symmetry system to account for polar anisotropy and azimuthal anisotropy. We have focused on the model made up of two welded ORT half-spaces to analyze the R/T coefficients normalized by vertical energy flux. The two half-spaces have azimuthally nonaligned vertical symmetry planes and are parameterized in two local 3D Cartesian coordinate frames, respectively. The vertical coordinate planes in each local frame coincide with the vertical symmetry planes for the corresponding ORT half-spaces. Under the weak contrast assumption for the two half-spaces, this model is taken as the perturbed model in R/T approximations with the perturbation theory. The unperturbed model is also composed of two unperturbed ORT half-spaces with their different vertical symmetry plane orientations inheriting the counterparts for the perturbed half-spaces above and below the interface, respectively. The unperturbed ORT half-spaces above and below the interface have the same model parameters defined in the two local coordinate frames, respectively. With the perturbations respectively evaluated in the local coordinate frames above and below the interface, the azimuth angle that indicates the local frames’ azimuthal difference is decoupled from the model parameter contrasts. Compared with the traditional approximation method with the perturbation theory in a global coordinate frame, the proposed R/T approximations depend on fewer model parameter discontinuities. We also consider the isotropic background medium under the weak anisotropy assumption. Influences of S-wave singularity points are mitigated by introducing pseudowaves for approximations. Numerical tests are implemented to demonstrate the accuracy.

Performing data fusion requires estimates of the state of a system to be converted to a common representation. The mean and covariance representation is the lingua franca of modern systems engineering. In particular, the covariance intersection (CI) 2 and Kalman lter (KF)3 algorithms provide mechanisms for fusing state estimates de ned in terms of means and covariances, where each mean vector de nes the nominal state of the system and its associated error covariance matrix de nes a lower bound on the squared error. However, most data fusion applications require the fusion of mean and covariance estimates de ning the state of a system in different coordinate frames. For example, a tracking system might maintain estimates in a global Cartesian coordinate frame, whereas observations of the tracked objects are generated in the local coordinate frames of various sensors. Therefore, a transformation must be applied to convert between the global coordinate frame and each local coordinate frame.

This paper studies the calibration problem of the transformation relationship between local coordinate frames in a distributed multi-agent system. The agents can only measure the bearing information and no global information is shared among all the agents. With the data sampled discretely, we first solve the transformation relationship by building linear equations. It turns out that the uniqueness of the solution plays a crucial role in the calibration problem. We then establish respectively the necessary conditions and sufficient conditions to solve the calibration problem. Experiments are conducted to prove the feasibility of the proposed calibration methods.

In this paper, the entrapping control problem of discrete-time AUVs with local coordinate frames is studied. To achieve entrapment in arbitrarily shaped orbits and formations, we design a bearing-based leader-following framework fully in the discrete-time domain with four parts: the orientation estimation unit, estimator unit, controller unit and parameters tuning unit. With bearing measurements and communication information, the orientation estimation unit can estimate orientations of local coordinate frames in finite time, and the estimator unit can achieve local localization. Based on estimation, the controller unit can drive each AUV to track the desired orbit or formation with an arbitrary shape. We present sufficient conditions under which stability of the overall system is proved using the theorem of finite-time stability and LaSalle’s theorem for the discrete-time system. Moreover, the parameters tuning unit can calculate optimal parameters to improve overall performance. Additionally, we extend our schemes to nonholonomic AUVs with unicycle models. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

Contouring control is crucial in high-speed and high-precision manufacturing. In this paper, a novel task polar coordinate frame (TPCF), moving along the desired contour, is proposed to naturally calculate and control the estimated contouring error by the circular approximation, a second-order approximation. The dynamics in the world Cartesian coordinate frame is transformed into radial and angular dynamics in the local polar coordinate frame. By the feedback linearization technique and an input feedforward compensation, the closed-loop dynamics are decoupled in terms of the estimated contouring error and the angular error, respectively. Proportional-plus-derivative controllers can be assigned to stabilize the individual axis dynamics in the TPCF. By tuning the control parameters, different strengthening on estimated contouring error and angular error can be imposed explicitly and directly. Various experiments on an XY-stage biaxial system with typical contours, a circle and a figure-“8,” were conducted. Comparative studies are carried out for the TPCF- and traditional Frenet frame-based controls. The contouring errors were drastically reduced by the proposed approach, particularly in high-speed and large-curvature contouring cases.

This paper studies the formation tracking control problem in the agents’ local co-ordinate frame without any special assumption, such as positive definiteness, on the initial orientation matrix. When follower agents do not have knowledge of their absolute orientation with respect to a global reference frame, formation control is difficult and special assumptions on initial orientation matrix are generally imposed for orientation synchronization. To address this, a distributed fixed time orientation synchronization law is first presented, using only relative orientation measurements, which aligns the co-ordinate frames of agents almost globally in finite time and locally in fixed time. This law is then used in cascade with an acceleration command for formation tracking control in a leader-follower set-up. Global asymptotic convergence of formation tracking error is proved for displacement based formation. For bearing-only formation control, semi-global uniformly asymptotic stability is established. Simulations illustrate the applicability of the results.

Prescribed performance distance-based formation control of Multi-Agent Systems

This letter studies formation control using bearing-only measurements for elevation angle rigid configurations in the presence of time-varying bounded disturbances. Elevation angle rigidity-based control laws ensure bearing-only formation control in agents’ local frame of reference sans any orientation synchronization or orientation estimation algorithms. However, existing control laws do not account for bounded disturbances in the agents’ dynamics. Motivated by this, we design bearing-only control laws for single integrators in agents’ frame of reference and prove local finite-time convergence to the desired formation. Then control laws for double integrators are proposed, and local asymptotic stability is proved when agents’ accelerations are affected by bounded disturbances. Simulations are provided to validate the claims.

In this paper, we present the experimental testing results of distributed cooperative control algorithms for multiple mobile robots with limited sensing/communication capacity and kinematic constraints. In the proposed distributed control, the input/output linearization via feedback is used to deal with nonlinear robot model constraints, and accordingly the linear distributed control is applied based on robots' current position and information exchange with their neighbors. The information exchange is done through a strategy accommodating the local sensing/communication capability of the robot platform used in the experiments. In other words, there is no a centralized system used in the experiments for localization. Instead, images acquired by the robot's own onboard Kinect sensor are used to convert the initial positions in robots' local coordinate frames into those in a global coordinate frame. Then the position data are communicated with neighboring robots via an ad-hoc peer-to-peer wireless TCP/IP connection for execution of distributed control rules. The experiments successfully demonstrate the practical implementation of our developed cooperative control algorithms through which both rendezvous and formation control problems are addressed.

This paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations and under possible occlusion and/or appearance of new objects. It presents a set of local absolute affine invariants derived from the convex hull of scattered feature points (e.g., fiducial or marking points, corner points, inflection points, etc.) extracted from the image. The affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices (quadruplets) of the convex hull, and hence do make direct use of the area invariance property associated with the affine transformation. Because they are locally constructed, they are very well suited to handle the occlusion and/or appearance of new objects. These invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them. A point matching approach for recognition follows this. The time complexity for registering L feature points on the test image with N feature points of the reference image is of order O(N x L). The method has been tested on real indoor and outdoor images and performs well.

In this chapter we present experimental results concerning identification of dynamic parameters of a load hold by a robot. There are ten dynamic parameters of the load namely mass, three parameters of the centre of mass multiplied by its mass, and six parameters of the inertia tensor, all together, ten parameters. These parameters are expressed in local coordinate frame which is associated with the load and therefore they are constant. Experimental identification of this set of parameters is quite difficult because we need very specialised equipment in order to carry out the experiments. Of course we can measure and weigh the load and then calculate all the parameters, but we want to do it experimentally, during the movement of the robot, assuming that the robot grasps the load which is a completely unknown object. The most expensive part is the force/torque sensor which has to be mounted between the wrist and the gripper. As mentioned in Chapter 2 Chair of Control, Robotics, and Computer Science has two force/torque sensors. The sensor allows us to measure forces and torques in the local coordinate frame associated with it. Three components of the forces and torques are measured in three dimensional space. Note, that in case considered here we need measurements of the forces and torques in three dimensions because these forces and torques are not compensated for by the structure of the gripper. In the case of joint generalised forces measurements, we can assume that the sensor measures only the forces and torques along the axis of translation and rotation, respectively.

Free-form design using axial curve-pairs

Linear kinematics model based on POE formula has been widely applied to the error compensation of robot. In this paper, we employed a calibration model in the Local POE frame where all the joint axes are repressed in their respective local frames. The major advantage of this formula is that the local coordinate frames can be arbitrarily assigned onto their corresponding links. For analyzing the applicability of linear model, this paper builds envelope model of error distribution using linear and second-order error model. Meanwhile, this paper analyzes Kuka Youbot robot's error distribution through the established model. The results show that the second-order model could be neglected in comparison with first-order model, when nominal error values of the joint angles are less than 0.1 degree. Hence, linear error model is enough precise in most real applicable environments.

We present a local affine-based adaptive regularization approach as an alternative to the homogeneous regularization used in Thirion's demons non-rigid registration algorithm, which does not preserve the deformation field discontinuities related to the independent motion of different organs, as typically occurs during CT and MR imaging of the abdomen and pelvis. By contrast, our method fits local affine transformation to each voxel; identifies the discontinuities between the locally fitted affine transformations; and adaptively smooths the deformation field, while preserving its local affine discontinuities. Experimental results on both synthetic and real CT images demonstrate that our method at once yields a smoother deformation field and preserves registration accuracy.

In this paper a strategy for controlling a group of agents to achieve positional consensus is presented. The proposed technique is based on the constraint that every agents must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming formulation that is computationally less intensive than earlier proposed methods. Moreover, we introduce a random perturbation input in the control command that helps us to achieve perfect consensus even for a large number of agents, which was not possible with the existing strategy in the literature. Moreover, we extend the method to achieve positional consensus at a pre-specified location. The effectiveness of the approach is illustrated through simulation results.