Particle Computation: Complexity, Algorithms, and Logic

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of obstacles to the environment can be used to create complex systems. We provide a wide range of results for a wide range of questions. These can be subdivided into external algorithmic problems, in which particle configurations serve as input for computations that are performed elsewhere, and internal logic problems, in which the particle configurations themselves are used for carrying out computations. For external algorithms, we give both negative and positive results. If we are given a set of stationary obstacles, we prove that it is NP-hard to decide whether a given initial configuration of unit-sized particles can be transformed into a desired target configuration. Moreover, we show that finding a control sequence of minimum length is PSPACE-complete. We also work on the inverse problem, providing constructive algorithms to design workspaces that efficiently implement arbitrary permutations between different configurations. For internal logic, we investigate how arbitrary computations can be implemented. We demonstrate how to encode dual-rail logic to build a universal logic gate that concurrently evaluates and, nand, nor, and or operations. Using many of these gates and appropriate interconnects, we can evaluate any logical expression. However, we establish that simulating the full range of complex interactions present in arbitrary digital circuits encounters a fundamental difficulty: a fan-out gate cannot be generated. We resolve this missing component with the help of 2x1 particles, which can create fan-out gates that produce multiple copies of the inputs. Using these gates we provide rules for replicating arbitrary digital circuits.Comment: 27 pages, 19 figures, full version that combines three previous conference article

Robust grasping under object pose uncertainty

This paper presents a decision-theoretic approach to problems that require accurate placement of a robot relative to an object of known shape, such as grasping for assembly or tool use. The decision process is applied to a robot hand with tactile sensors, to localize the object on a table and ultimately achieve a target placement by selecting among a parameterized set of grasping and information-gathering trajectories. The process is demonstrated in simulation and on a real robot. This work has been previously presented in Hsiao et al. (Workshop on Algorithmic Foundations of Robotics (WAFR), 2008; Robotics Science and Systems (RSS), 2010) and Hsiao (Relatively robust grasping, Ph.D. thesis, Massachusetts Institute of Technology, 2009).National Science Foundation (U.S.) (Grant 0712012

A General Stance Stability Test Based on Stratified Morse Theory With Application to Quasi-Static Locomotion Planning

This paper considers the stability of an object supported by several frictionless contacts in a potential field such as gravity. The bodies supporting the object induce a partition of the object's configuration space into strata corresponding to different contact arrangements. Stance stability becomes a geometric problem of determining whether the object's configuration is a local minimum of its potential energy function on the stratified configuration space. We use Stratified Morse Theory to develop a generic stance stability test that has the following characteristics. For a small number of contacts---less than three in 2-D and less than six in 3-D---stance stability depends both on surface normals and surface curvature at the contacts. Moreover, lower curvature at the contacts leads to better stability. For a larger number of contacts, stance stability depends only on surface normals at the contacts. The stance stability test is applied to quasi-static locomotion planning in two dimensions. The region of stable center-of-mass positions associated with a $k$-contact stance is characterized. Then, a quasi-static locomotion scheme for a three-legged robot over a piecewise linear terrain is described. Finally, friction is shown to provide robustness and enhanced stability for the frictionless locomotion plan. A full maneuver simulation illustrates the locomotion scheme

Review. Technologies for robot grippers in pick and place operations for fresh fruits and vegetables

[EN] Robotics has been introduced in industry to replace humans in arduous and repetitive tasks, to reduce labour costs and to ensure consistent quality control of the process. Nowadays robots are cheaper, can work in hostile and dirty environments and they are able to manipulate products at high speed. High speed and reliability and low robot gripper costs are necessary for a profitable pick and place (P&P) process. However, current grippers are not able to handle these products properly because they have uneven shapes, are flexible and irregular, have different textures and are very sensitive to being damaged. This review brings together the requirements and phases used in the process of manipulation, summarises and analyses of the existing, potential and emerging techniques and their possibilities for the manipulation of fresh horticultural products from a detailed study of their characteristics. It considers the difficulties and the lack of engineers to conceive of and implement solutions. Contact grippers with underactuated mechanism and suction cups could be a promising approach for the manipulation of fresh fruit and vegetables. Ongoing study is still necessary on the characteristics and handling requirements of fresh fruit and vegetables in order to design grippers which are suitable for correct manipulation, at high speed, in profitable P&P processes for industrial applications.This work has been partially funded by research project with reference DPI2010-20286 financed by the Spanish Ministerio de Ciencia e Innovacion.Blanes Campos, C.; Mellado Arteche, M.; Ortiz Sánchez, MC.; Valera Fernández, Á. (2011). Review. Technologies for robot grippers in pick and place operations for fresh fruits and vegetables. SPANISH JOURNAL OF AGRICULTURAL RESEARCH. 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Using Partial Sensor Information to Orient Parts

Parts orienting, the process of bringing parts in initially unknown orientations to a goal orientation, is an important aspect of automated assembly. The most common industrial orienting systems are vibratory bowl feeders, which use the shape and mass properties of parts to orient them. Bowl feeders rely on a sequence of mechanical operations and typically do not use sensors. In this paper, we describe the use of partial information sensors along with a sequence of pushing operations to eliminate uncertainty in the orientations of parts. We characterize the shorter execution lengths of sensor-based plans and show that sensor-based plans are more powerful than sensorless plans in that they can bring a larger class of parts to distinct orientations