On the numerical classification of the singularities of robot manipulators

This paper is concerned with the task to obtain a complete description of the singularity set of any given non-redundant manipulator, including the identification and the precise computation of each constituent singularity class. Configurations belonging to the same class are equivalent in terms of the various types of kinematic and static degeneracy that characterize mechanism singularity. The proposed approach is an extension of recent work on computing singularities using a numerical method based on linear relaxations. Classification is sought by means of a hierarchy of singularity tests, each formulated as a system of quadratic or linear equations, which yields sets of classes to which an identified singularity cannot belong. A planar manipulator exemplifies the process of classification, and illustrates how, while most singularities get completely classified, for some lower-dimensional subsets one can only identify a restricted list of possible singularity classes.Postprint (published version

coordinated selection and timing of multiple trajectories of discretely mobile robots

Abstract The paper addresses the multi-agent path planning (MPP) of mobile agents with multiple goals taking into consideration the kinematic constraints of each agent. The "Swing and Dock" (SaD) robotic system being discussed uses discrete locomotion, where agents swing around fixed pins and dock with their mounting legs to realize displacement from one point to another. The system was developed as a subsystem for mobile robotic fixture (SwarmItFix). Previous work dealt with MPP for SaD agents using the concept of extended temporal graph with Integer Linear Programming (ILP) based formulations. The approach discretized time into unit steps, whereas in reality, the agents are constrained by velocity limits. Hence, a real-time schedule is required to accurately plan the agent movement in a working scenario. We utilize the concept of simple temporal network and extend our ILP formulations to model the velocity kinematic constraints. The mathematical formulations are implemented and tested using a GUROBI solver. Computational results display the effectiveness of the approach

The SwarmItFix Pilot

Abstract The paper presents the integration and experiments with a pilot cell including a traditional machine tool and an innovative robot-swarm cooperative conformable support for aircraft body panels. The pilot was installed and tested in the premises of the aircraft manufacturer Piaggio Aerospace in Italy. An original approach to the support of the panels is realized: robots with soft heads operate from below the panel; they move upward the panel where manufacturing is performed, removing the sagging under gravity and returning it to its nominal geometry; the spindle of amilling machine performs the machining from above

Generalized singularity analysis of mechanisms

grantor: University of TorontoThis thesis investigates a general class of mechanism configurations, usually referred to as kinematic singularities. The study of such configurations is of major practical and theoretical importance. Indeed, the kinematic properties of mechanisms change significantly in a singular configuration, and these changes can prove to be either beneficial or undesirable for different applications. On the other hand, the theoretic significance of singularities in mechanism theory is well-known and related to the fact that singular points play a prominent role in the theory of differentiable mappings. The central objective of this dissertation is to address the problems of mechanism singularity in a most general setting, namely, to consider arbitrary singular configurations of both non-redundant and redundant mechanisms with arbitrary kinematic chains, with a special emphasis on the study of mechanical devices with complex kinematic chains and non-serial, high-degree-of-freedom architectures. To this goal, a rigorous general mathematical definition of kinematic singularity for arbitrary mechanisms is introduced. This is achieved by means of a mathematical model of mechanism kinematics formulated in terms of differentiable mappings between manifolds. When the mathematical model is applied to the relationship between the joint and output velocities, a new unifying framework for the interpretation and classification of mechanism singularities is obtained. This framework, based on the newly introduced six singularity types, is applicable to arbitrary non-redundant as well as redundant mechanisms. Mathematical tools, such as singularity criteria and identification methods, are developed for the study of the singularity sets of both non-redundant and redundant systems with lower kinematic pairs.Ph.D