Monte Carlo algorithms for the detection of necessary linear matrix inequality constraints

We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor. A necessary LMI is one whose removal changes the feasible region defined by all the LMI constraints. The general problem of checking whether or not a particular LMI is necessary is NP-complete. However, the methods we describe are polynomial in each iteration, and the number of iterations can be limited by stopping rules. This provides a practical method for reducing the size of some large Semidefinite Programming problems before one attempts to solve them. We demonstrate the applicability of this approach to solving instances of the Lowner ellipsoid problem. We also consider the problem of classification of all the constraints of a semidefinite programming problem as redundant or necessary

Multisensor-based human detection and tracking for mobile service robots

The one of fundamental issues for service robots is human-robot interaction. In order to perform such a task and provide the desired services, these robots need to detect and track people in the surroundings. In the present paper, we propose a solution for human tracking with a mobile robot that implements multisensor data fusion techniques. The system utilizes a new algorithm for laser-based legs detection using the on-board LRF. The approach is based on the recognition of typical leg patterns extracted from laser scans, which are shown to be very discriminative also in cluttered environments. These patterns can be used to localize both static and walking persons, even when the robot moves. Furthermore, faces are detected using the robot's camera and the information is fused to the legs position using a sequential implementation of Unscented Kalman Filter. The proposed solution is feasible for service robots with a similar device configuration and has been successfully implemented on two different mobile platforms. Several experiments illustrate the effectiveness of our approach, showing that robust human tracking can be performed within complex indoor environments