In this paper, we consider the precoder design for an underloaded or critically loaded downlink multi-user multiple-input multiple-output (MIMO) communication system. We propose novel precoding and decoding schemes which enhance system performance based on rate splitting at transmitter single-stage successive interference cancellation receivers. The proposed null-space (SNS) utilizes linear com...

Given a matrix, the Null Space Problem asks for a basis of its null space having the fewest nonzeros. This problem is known to be NP-complete and even hard to approximate. The null space of a forest is the null space of its adjacency matrix. Sander and Sander (2005) and Akbari et al. (2006), independently, proved that the null space of each forest admits a {−1, 0, 1}-basis. We devise an algorit...

Null space velocity control is essential for achieving good behaviour of a redundant manipulator. Using the dynamically consistent pseudo-inverse, the task and null space motion and forces are decoupled. The paper presents a globally stable null space velocity controller and the gradient projection technique in conjunction with the dynamically consistent pseudo-inverse. The physical meaning and...

Given a set of h pairwise disjoint polygonal obstacles of totally n vertices in the plane, we study the problem of computing an L1 (or rectilinear) shortest path between two points avoiding the obstacles. Previously, this problem has been solved in O(n log n) time and O(n) space, or alternatively in O(n + h log n) time and O(n + h log h) space. A lower bound of Ω(n + h log h) time and Ω(n) spac...

In many fields of application, shortest path finding problems in very large graphs arise. Scenarios where large numbers of on-line queries for shortest paths have to be processed in real-time appear for example in traffic information systems. In such systems, the techniques considered to speed up the shortest path computation are usually based on precomputed information. One approach proposed o...

—Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are nonholonomic and, in 2D, equivalent to a Dubins car with constant radius of curvature. In 3D, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle. We present a constant-time mot...

Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are nonholonomic and, in 2D, equivalent to a Dubins car with constant radius of curvature. In 3D, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle.We present a constant-time motio...

In recent years, a number of tools have become available that recover the underlying control policy from constrained movements. However, few have explicitly considered learning the constraints of the motion and ways to cope with unknown environment. In this paper, we consider learning the null space projection matrix of a kinematically constrained system in the absence of any prior knowledge ei...