Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to their ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the performance of the existing FW method hinges on the quality of the linear approximation. This typically restricts FW to smooth functions for which the approximation quality, indicated by a global curvature measure, is reasonably good. In this paper, we propose a modified FW algorithm amenable to nonsmooth functions, subject to a separability assumption, by optimizing for approximation quality over all affine functions, given a neighborhood of interest. We analyze theoretical properties of the proposed algorithm and demonstrate that it overcomes many issues associated with existing methods in the context of nonsmooth low-rank matrix estimation.

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method for nuclear norm constrained problems. The goal is to generate descent steps that lead to rank decreases, maintaining low-rank solutions throughout the algorithm. Moreover, the optimization problems are constrained to ensure that the rank-drop step is also feasible and can be readily incorporated into a projection-free minimization method, e.g., Frank-Wolfe. We demonstrate that by incorporating rank-drop steps into the Frank-Wolfe algorithm, the rank of the solution is greatly reduced compared to the original Frank-Wolfe or its common variants.

The Semi-Supervised Support Vector Machine (S3VM) solves a non-convex, Mixed-Integer Program (MIP). Due to difficulty in solving the problem, convex approximations have typically been used. However, existing approaches suffer from poor scalability and struggle on certain datasets, compared to graph based counterparts. The poor predictive performance suggests that for some datasets, convex approximations may not be a sufficiently accurate approximation to the problem. We present a self-training approach with self-adapting regularization parameters for S3VM formulations. At each iteration, the regularization parameters are adapted to better reflect label confidence, class proportion, and to gradually include more unlabeled points. We show that updating the S3VM framework iteratively in this fashion, the sequence of SVM subproblems can be solved very efficiently and the solution generated by this sequence yields superior performance compared to leading SSL methods.

The problem of generating collision-free motion in an operator-assisted teleoperated robot arm manipulator system is discussed. The concentration is on several system requirements: a real real-time operation, a guarantee of collision-free motion for the entire body of the arm manipulator, and an ability to handle obstacles of arbitrary shapes. The suggested methodology draws on recent work on motion planning with incomplete information for whole-sensitive robots.>

Recent results in sensor-based motion planning suggest that the collision avoidance task can be handled automatically, thus freeing the operator for global control. Whole-sensitive arm manipulators bodies are covered with a sensitive skin sensor to detect nearby objects are proposed for this purpose. The data from the sensitive skin is used with the sensor data processing and motion planning algorithms to avoid collisions for the entire robot arm body in an unknown or time-varying environment. The result is a highly efficient, safe, and robust hybrid system in which the shift motion control between the operator and the automatic system is done transparently and in real-time. The motion of the master arm is either executed faithfully, or, to avoid collisions, is used as general guidance for the slave arm.>

A sensor-based motion planning system for a robot arm manipulator must include these four basic components: sensor hardware; real-time signal/sensory data processing hardware/software a local step planning subsystem that works at the basic sample rate of the arm; and a subsystem for global planning. The objective of this work is to develop the fourth component, a real-time implementable algorithm that realizes the upper, global level of planning. Based on the current collection of local normals, the algorithm generates preferable directions of motion around obstacles, in order to guarantee reaching the target position if it is reachable. Experimental results from testing the developed system are also discussed.>

The authors describe an ongoing research project on the development of a sensitive skin and its control scheme for a 3D robot arm. The skin consists of hundreds of active infrared proximity sensors that cover the whole arm. This sensor-based motion planning system senses obstacles by emitting amplitude-modulated infrared light and then sensing the reflected signal. The problem of interpreting data from the sensors is handled by the step planning algorithm, which transforms the sensor data into local tangent normals in the configuration space. Once this information is available, a global path planning algorithm can then be used to move the arm through freespace or to follow the contour of obstacles that are encountered. Details of the skin design are presented, along with the computer hardware and operating logistics and the sensor data interpretation algorithm that connects this subsystem to the global motion planning subsystem.>

Results of one effort to implement a motion planning system for a robot arm operating in an uncertain environment are discussed. It is known that path planning algorithms with proven convergence can be designed for some planar and three-dimensional robot arm manipulators operating among unknown obstacles of arbitrary shapes. The attractiveness of such systems lies in their ability to operate in a complex, perhaps even time-varying, unstructured environment. Implementation of these algorithms, however, presents a variety of hardware and algorithmic problems related to: covering the arm with arrays of sensors to form a sensitive skin; processing real-time sensor data; designing complementary algorithms for step-by-step motion planning based on limited local information; and integrating these components, together with global planning algorithms, in a single system. The authors discuss various tradeoffs and solutions implemented in the sensor-based planning system for a planar arm manipulator developed in their laboratory and present a summary of their experiments with it.>

The problem of sensor-based path planning for robot arm manipulators operating among unknown obstacles of arbitrary shape is considered. It has been known that, in principle, algorithms with proven convergence can be designed for planar and simple three-dimensional robot arms operating under such conditions. However, implementation of these algorithms presents a variety of hardware and algorithmic problems related to covering the robot arm with a sensitive skin, processing data from large arrays of sensors, and designing algorithms for step-by-step motion planning based on limited information. The authors describe the hardware and the lower-level control algorithms of a system for robot motion planning in an uncertain environment and summarize results of experiments with the system.>