Kinematic topology and constraints of multi-loop linkages

SUMMARYModeling the instantaneous kinematics of lower pair linkages using joint screws and the finite kinematics with Lie group concepts is well established on a solid theoretical foundation. This allows for modeling the forward kinematics of mechanisms as well the loop closure constraints of kinematic loops. Yet there is no established approach to the modeling of complex mechanisms possessing multiple kinematic loops. For such mechanisms, it is crucial to incorporate the kinematic topology within the modeling in a consistent and systematic way. To this end, in this paper a kinematic model graph is introduced that gives rise to an ordering of the joints within a mechanism and thus allows to systematically apply established kinematics formulations. It naturally gives rise to topologically independent loops and thus to loop closure constraints. Geometric constraints as well as velocity and acceleration constraints are formulated in terms of joint screws. An extension to higher order loop constraints is presented. It is briefly discussed how the topology representation can be used to amend structural mobility criteria.

Incremental Loop Closure Verification by Guided Sampling

Loop closure detection, which is the task of identifying locations revisited by a robot in a sequence of odometry and perceptual observations, is typically formulated as a combination of two subtasks: (1) bag-of-words image retrieval and (2) post-verification using random sample consensus (RANSAC) geometric verification. The main contribution of this study is the proposal of a novel post-verification framework that achieves good precision recall trade-off in loop closure detection. This study is motivated by the fact that not all loop closure hypotheses are equally plausible (e.g., owing to mutual consistency between loop closure constraints) and that if we have evidence that one hypothesis is more plausible than the others, then it should be verified more frequently. We demonstrate that the loop closure detection problem can be viewed as an instance of a multi-model hypothesize-and-verify framework. Thus, we can build guided sampling strategies on this framework where loop closures proposed using image retrieval are verified in a planned order (rather than in a conventional uniform order) to operate in a constant time. Experimental results using a stereo simultaneous localization and mapping (SLAM) system confirm that the proposed strategy, the use of loop closure constraints and robot trajectory hypotheses as a guide, achieves promising results despite the fact that there exists a significant number of false positive constraints and hypotheses.

Representation of the kinematic topology of mechanisms for kinematic analysis

The kinematic modeling of multi-loop mechanisms requires a systematic representation of the kinematic topology, i.e. the arrangement of links and joints. A linear graph, called the topological graph, is used to this end. Various forms of this graph have been introduced for application in mechanism kinematics and multibody dynamics aiming at matrix formulations of the governing equations. For the (higher-order) kinematic analysis of mechanisms a simple yet stringent representation of the topological information is often sufficient. This paper proposes a simple concept and notation for use in kinematic analysis. Upon a topological graph, an order relation of links and joints is introduced allowing for recursive computation of the mechanism configuration. An ordering is also introduced on the topologically independent fundamental cycles. The latter is indispensable for formulating generically independent loop closure constraints. These are presented for linkages with only lower pairs, as well as for mechanisms with one higher kinematic pair per fundamental cycle. The corresponding formulation is known as cut-body and cut-joint approach, respectively.

Folding Rigid Origami With Closure Constraints

Rigid origami is a class of origami whose entire surface remains rigid during folding except at crease lines. Rigid origami finds applications in manufacturing and packaging, such as map folding and solar panel packing. Advances in material science and robotics engineering also enable the realization of self-folding rigid origami and have fueled the interests in computational origami, in particular the issues of foldability, i.e., finding folding steps from a flat sheet of crease patterns to desired folded state. For example, recent computational methods allow rapid simulation of folding process of certain rigid origamis. However, these methods can fail even when the input crease pattern is extremely simple. This paper attempts to address this problem by modeling rigid origami as a kinematic system with closure constraints and solve the foldability problem through a randomized method. Our experimental results show that the proposed method successfully fold several types of rigid origamis that the existing methods fail to fold.

Acceleration Analysis of 3DOF Parallel Manipulators

This paper presents a new approach to the velocity and acceleration analyses 3DOF parallel manipulators. Building on the definition of the ‘acceleration motor’, the forward and inverse velocity and acceleration equations are formulated such that the relevant analysis can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3- PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulators

This paper presents a new approach to the velocity and acceleration analyses of lower mobility parallel manipulators. Building on the definition of the “acceleration motor,” the forward and inverse velocity and acceleration equations are formulated such that the relevant analyses can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.