Kinematic topology and constraints of multi-loop linkages

Robotica ◽  
2018 ◽  
Vol 36 (11) ◽  
pp. 1641-1663 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Theoretical Foundation ◽  
Kinematic Model ◽  
Geometric Constraints ◽  
Loop Closure ◽  
Lower Pair ◽  
Kinematic Loops ◽  
Structural Mobility ◽  
Loop Constraints ◽  
Model Graph ◽  
Closure Constraints

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.

scholarly journals A Novel Loop Closure Detection Approach Using Simplified Structure for Low-Cost LiDAR

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2299
Author(s):  
Qin Ye ◽  
Pengcheng Shi ◽  
Kunyuan Xu ◽  
Popo Gui ◽  
Shaoming Zhang
Keyword(s):  
Point Cloud ◽  
Detection Efficiency ◽  
Low Cost ◽  
Evaluation Model ◽  
Level Structure ◽  
Geometric Constraints ◽  
Global Localization ◽  
Point Cloud Registration ◽  
Loop Closure ◽  
Loop Closure Detection

Reducing the cumulative error is a crucial task in simultaneous localization and mapping (SLAM). Usually, Loop Closure Detection (LCD) is exploited to accomplish this work for SLAM and robot navigation. With a fast and accurate loop detection, it can significantly improve global localization stability and reduce mapping errors. However, the LCD task based on point cloud still has some problems, such as over-reliance on high-resolution sensors, and poor detection efficiency and accuracy. Therefore, in this paper, we propose a novel and fast global LCD method using a low-cost 16 beam Lidar based on “Simplified Structure”. Firstly, we extract the “Simplified Structure” from the indoor point cloud, classify them into two levels, and manage the “Simplified Structure” hierarchically according to its structure salience. The “Simplified Structure” has simple feature geometry and can be exploited to capture the indoor stable structures. Secondly, we analyze the point cloud registration suitability with a pre-match, and present a hierarchical matching strategy with multiple geometric constraints in Euclidean Space to match two scans. Finally, we construct a multi-state loop evaluation model for a multi-level structure to determine whether the two candidate scans are a loop. In fact, our method also provides a transformation for point cloud registration with “Simplified Structure” when a loop is detected successfully. Experiments are carried out on three types of indoor environment. A 16 beam Lidar is used to collect data. The experimental results demonstrate that our method can detect global loop closures efficiently and accurately. The average global LCD precision, accuracy and negative are approximately 0.90, 0.96, and 0.97, respectively.

scholarly journals Implementation of A Geometric Constraint Regularization For Multibody System Models

2014 ◽  
Vol 61 (2) ◽  
pp. 365-383 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Multibody System ◽  
Time Integration ◽  
Simulation Method ◽  
Dynamics Simulation ◽  
Computational Performance ◽  
Kinematic Loops ◽  
Computationally Expensive ◽  
Technical Systems ◽  
Loop Constraints

Abstract Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.

scholarly journals Incremental Loop Closure Verification by Guided Sampling

2017 ◽  
Vol 21 (1) ◽  
pp. 59-66
Author(s):  
Tanaka Kanji ◽  
Keyword(s):  
Image Retrieval ◽  
Good Precision ◽  
Sampling Strategies ◽  
Detection Problem ◽  
Loop Closure ◽  
Loop Closure Detection ◽  
Robot Trajectory ◽  
Localization And Mapping ◽  
Random Sample Consensus ◽  
Closure Constraints

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.

New constraints on the tectonic activity of the “Tellian Domain” from Northern Tunisia: preliminary paleomagnetic results.

2020 ◽  
Author(s):  
Philippe Robion ◽  
Marwen Arfaoui ◽  
Riadh Ahmadi ◽  
Mohamed El Messaoud Derder ◽  
Mohamed Amena ◽  
...  
Keyword(s):  
Rock Magnetism ◽  
Kinematic Model ◽  
Sedimentary Rocks ◽  
Vertical Axis ◽  
Geometric Constraints ◽  
Tectonic Activity ◽  
North West ◽  
North East ◽  
Magnetization Intensity ◽  
Characteristic Component

<p>In this study, we present preliminary results on paleomagnetic data collected in the Tunisian Tellian domain in both magmatic and sedimentary rocks of middle to lat Miocene ages from the Nefza-Mogods province, North-West of Tunisia. About 320 cores distributed over twenty one sites were collected both in magmatic rocks (16 sites) and in sedimentary rocks (5 sites), in order to obtain geometric constraints to establish a kinematic model along the North-East African margin. The sampled rocks are distributed between basanites, rhyodacites and microgranites. Some samples were taken from host sedimentary rocks host rocks in lacustrine limestones and jaspilites. Demagnetization process and Rock-Magnetism studies revealed a diversified magnetic mineralogy. In basalts, magnetite with an unblocking temperature of 580 °C is identified. In rhyodacites, the mineralogy is mixed with three types of minerals: a mineral with an unblocking temperature around 350°-400°C attributed either to a sulfide or to titanomagnetite, magnetite with unblocking temperature at 580°C, and a high temperature mineral with unblocking temperature between 600°C and 680°C attributed to hematite or titanohematite. The limestones, having a low magnetization intensity, are characterized by the presence of magnetite and the jaspilites by hematite. Basalts, which have been mainly demagnetized by AF process , show a characteristic component demagnetized between 20mT and 100mT. For rhyodacites, some sites have a characteristic component demagnetized between 400°C and 580°C and others up to 670°C. Although their low magnetization intensity, the lacustrine limestones show a magnetic component between 20mT and 140 mT. The first result indicate that the mean directions associated to the younger magmatic (basalts and rhyodacite) rocks (8 Ma, Tortonian) and their sedimentary host deposits are very close to the expected magnetic field after tilting in paleogeographic coordinates. By contrast, the older microgranites and rhyodacites(-12 Ma) display a vertical axis clockwise rotation of about 30°. This result suggests a significant tectonic phase between 12 Ma and 8 Ma, linked to the implementation of the Tell nappes.</p>

scholarly journals A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping

2018 ◽  
Vol 23 (4) ◽  
pp. 74 ◽  
Author(s):  
Roland Zana ◽  
Bálint Bodor ◽  
László Bencsik ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Legged Locomotion ◽  
Rigid Bodies ◽  
Pattern Generation ◽  
Constrained Systems ◽  
Piecewise Smooth ◽  
Geometric Constraints ◽  
Mathematical Representation ◽  
Differential Algebraic Equation ◽  
Kinematic Loops

Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results.

Incorporating Fixed-Point and -Line Constraints and Tolerance Based Synthesis in 4MDS

2015 ◽  
Author(s):  
Anurag Purwar ◽  
Saurabh Bhapkar ◽  
Q. J. Ge
Keyword(s):  
Theoretical Foundation ◽  
Geometric Constraints ◽  
Machine Design ◽  
Design Stage ◽  
Design System ◽  
Motion Synthesis ◽  
Kinematic Mapping ◽  
Line Tangent ◽  
Fixed Line ◽  
Best Fit

This paper presents implementation of fixed-pivots, ground-link line, and tolerance based motion synthesis in the 4MDS (Four-Bar Motion Design System). This is a continuation of the first work reported on 4MDS, which provides an interactive, graphical, and geometric constraint based mechanism design system for the exact- and approximate-motion synthesis problems. Theoretical foundation of the 4MDS is laid over a kinematic mapping based unified formulation of the geometric constraints (circle, fixed-line, line-tangent-to-a-circle) associated with the mechanical dyads (RR, PR, and RP) of a planar four-bar mechanism. An efficient algorithm extracts the geometric constraints of a given motion task and determines the best dyad types as well as their dimensions that best fit to the motion. Often, Mechanism designers need to impose additional geometric constraints, such as specification of location of fixed pivots or ground-link line. If synthesized mechanism suffers from branch, circuit, or order defect, they may also desire rectified solutions by allowing a tolerance to certain or all task positions. Such functions are crucial to a practitioner and much needed during the conceptual design stage of machine design process.

Semialgebraic Regularization of Kinematic Loop Constraints in Multibody System Models

2011 ◽  
Vol 6 (4) ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Multibody System ◽  
Dynamics Simulation ◽  
Time Step ◽  
Kinematic Loops ◽  
Low Dimensional ◽  
Kinematic Loop ◽  
Value Decomposition ◽  
Loop Constraints ◽  
Simulation Time

Redundant constraints in multibody system (MBS) models, reflected by a singular constraint Jacobian, impair the efficient dynamics simulation. In particular, kinematic loop constraints are often found to be permanently redundant. This problem is commonly attacked numerically by decomposing the constraint Jacobian either at every simulation time step or beforehand in an admissible assembly (assuming that the redundancy is permanent). This paper presents a method for the elimination of permanently redundant loop closure constraints, which, instead of numerically decomposing the constraints, relies on the geometric characterization of kinematic loops comprising lower kinematic pairs. In particular, the invariant vector space of velocities of a kinematic loop is taken into account, which can be determined as the sum of Lie (screw) algebras of two subchains of a kinematic loop. The actual reduction is achieved by restricting the constraints to this space. The presented method does not interfere with the actual generation of constraints but can be considered as a preprocessing step of MBS models. It is numerically robust and only uses a geometrically exact model. The method is able to completely eliminate redundant loop constraints for “nonparadoxical” single-loop mechanisms and applies conservatively to multiloop MBS. The presented method only requires information (vectors, matrices) that is readily available in any MBS simulation package. The only numerical operations involved are cross products and a singular value decomposition of a low dimensional matrix.

Sign in / Sign up

Export Citation Format

Share Document