Abstract-A sensor network localization problem is to determine the positions of the sensor nodes in a network given incomplete and inaccurate pairwise distance measurements. Such distance data may be acquired by a sensor node by communicating with its neighbors. We describe a general semidefinite programming (SDP) based approach for solving the graph realization problem, of which the sensor network localization problems is a special case. We investigate the performance of this method on problems with noisy distance data. Error bounds are derived from the SDP formulation. The sources of estimation error in the SDP formulation are identified.The SDP solution usually has a rank higher than the underlying physical space, which when projected onto the lower dimensional space generally results in high estimation error. We describe two improvements to ameliorate such a difficulty. First, we propose a regularization term in the objective function that can help to reduce the rank of the SDP solution. Second, we use the points estimated from the SDP solution as the initial iterate for a gradient-descent method to further refine the estimated points. A lower bound obtained from the optimal SDP objective value can be used to check the solution quality. Experimental results are presented to validate our methods and show that they outperform existing SDP methods.

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The manipulator with a large degree of redundancy is useful for realizing multiple tasks such as maneuvering the robotic arms in the constrained workspace, e.g. the task of maneuvering the end-effector of the manipulator along a pre-specified path into a window. This paper presents an on-line technique based on a posture generation rule to compute a null-space joint velocity vector in a singularity-robust redundancy resolution method. This rule suggests that the end of each link has to track an implicit trajectory that is indirectly resulted from the constraint imposed on tracking motion of the end-effector. A proper posture can be determined by sequentially optimizing an objective function integrating multiple criteria of the orientation of each link from the end-effector toward the base link as the secondary task for redundancy resolution, by assuming one end of the link is clamped. The criteria flexibly incorporate obstacle avoidance, joint limits, preference of posture in tracking, and connection of posture to realize a compromise between the primary and secondary tasks. Furthermore, computational demanding of the posture is reduced due to the sequential link-by-link computation feature. Simulations show the effectiveness and flexibility of the proposed method in generating proper postures for the collision avoidance and the joint limits as a singularity-robust null-space projection vector in maneuvering redundant robots within constrained workspaces.

This article studies the trajectory planning of redundant robots performing tasks within an enclosed workspace. Configuration control of kinematically redundant manipulators using the pseudo-inverse with null-space projection method is a wellknown scheme. One advantage of this method is that the gradient of an objective function can be included in the homogeneous term to optimize the objective function without affecting the position of the end-effector. Using different objective functions, this method can achieve redundancy resolution such as obstacle or joint limits avoidance. Along this line of redundancy resolution, a switching objective function is proposed. We modify Liegeois' joint angle availability objective function so that the midpoints of each joint are switched at a series of prespecified key path points for the end-effector to achieve. These key path points are planned beforehand according to the geometry of the constrained workspace. The trajectory planning problem can then Ž . be viewed as a series of proper postures i.e., midpoints determination problems at the key path points. The proper postures are determined using a combination of the potential field method and the elastic model method that takes into account joint operating ranges and the motion tendency of the end-effector. A variable weighting technique to achieve the proper postures effectively is also presented. Simulations of a planar eight-link robot in a constrained workspace illustrate the effectiveness of the switching objective function with the variable weighting approach in trajectory planning problems. ᮊ

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Ball passing is an elementary and frequently employed human soccer skill. This paper examines the realization and visualization of ball passing, a low level move-to-ball behavior of a soccer robot, in a robot soccer game. A case study of three mechanically identical mobile robots with a formation ready to pass a ball cyclically in a zigzag pattern is examined. We build a control command driven mobile robot motion simulator with a controller and dynamics of mobile robots, not only nonholonomic kinematic constraints to simulate the motion of a soccer robot driven by wheels torques to generate wheels accelerations, to update the robot position and orientation at successive time instants. Kick motion follows a physical law, and a simplified collision check and response model is utilized for the efficient detection of the hitting a robot with the ball or other robots. The realization of specific ball passing strategy to drive each soccer robot in a position to receive a pass includes three levels of organization, coordination, and execution: careful integrated design of a dynamic formation and role change scheme, ball position estimation, and coordinated trajectory (i.e. path and velocity) planning and tracking control. Simulations are performed to illustrate the feasibility of the realization of ball passing among three robots, implemented by a software program for coordinated trajectory planning and tracking control in the developed simulator.

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A motion control and the corresponded strategy to realize cyclic ball passing motion in robot soccer games are presented in this paper. By this strategy, multiple mobile robots kick the ball in tum with high speed while they adjust or change their formation. The ball-kick controller is to drive the robot to an adequate position with a prescribed velocity in a fixed finite time. After kicking, the robot is driven to a suitable position for next ball-passing movement and could accomplish other objectives in robot soccer games. A computer simulation using dynamical model of two-wheeled mobile robot demonstrates the feasibility of this method.