scholarly journals Motion Planning of a Second-Order Nonholonomic Chained Form System Based on Holonomy Extraction

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1337
Author(s):  
Masahide Ito
Keyword(s):  
Motion Planning ◽  
Nonholonomic Systems ◽  
Second Order ◽  
Literature Survey ◽  
First Order ◽  
Underactuated Manipulator ◽  
Planning Algorithm ◽  
The One ◽  
Specific Control ◽  
Form System

This paper proposes a motion planning algorithm for dynamic nonholonomic systems represented in a second-order chained form. The proposed approach focuses on the so-called holonomy resulting from a kind of motion that traverses a closed path in a reduced configuration space of the system. According to the author’s literature survey, control approaches that make explicit use of holonomy exist for kinematic nonholonomic systems but does not exist for dynamic nonholonomic systems. However, the second-order chained form system is controllable. Also, the structure of the second-order chained form system analogizes with the one of the first-order chained form for kinematic nonholonomic systems. These survey and perspectives brought a hypothesis that there exists a specific control strategy for extracting holonomy of the second-order chained form system to the author. To verify this hypothesis, this paper shows that the holonomy of the second-order chained form system can be extracted by combining two appropriate pairs of sinusoidal inputs. Then, based on such holonomy extraction, a motion planning algorithm is constructed. Furthermore, the effectiveness is demonstrated through some simulations including an application to an underactuated manipulator.

scholarly journals Sampling-Based Motion Planning for Free-Floating Space Robot without Inverse Kinematics

2020 ◽  
Vol 10 (24) ◽  
pp. 9137
Author(s):  
Hongwen Zhang ◽  
Zhanxia Zhu
Keyword(s):  
Motion Planning ◽  
Inverse Kinematics ◽  
Random Trees ◽  
Space Robot ◽  
Initial Configuration ◽  
First Order ◽  
System A ◽  
Planning Framework ◽  
Planning Algorithm ◽  
Differential Relationship

Motion planning is one of the most important technologies for free-floating space robots (FFSRs) to increase operation safety and autonomy in orbit. As a nonholonomic system, a first-order differential relationship exists between the joint angle and the base attitude of the space robot, which makes it pretty challenging to implement the relevant motion planning. Meanwhile, the existing planning framework must solve inverse kinematics for goal configuration and has the limitation that the goal configuration and the initial configuration may not be in the same connected domain. Thus, faced with these questions, this paper investigates a novel motion planning algorithm based on rapidly-exploring random trees (RRTs) for an FFSR from an initial configuration to a goal end-effector (EE) pose. In a motion planning algorithm designed to deal with differential constraints and restrict base attitude disturbance, two control-based local planners are proposed, respectively, for random configuration guiding growth and goal EE pose-guiding growth of the tree. The former can ensure the effective exploration of the configuration space, and the latter can reduce the possibility of occurrence of singularity while ensuring the fast convergence of the algorithm and no violation of the attitude constraints. Compared with the existing works, it does not require the inverse kinematics to be solved while the planning task is completed and the attitude constraint is preserved. The simulation results verify the effectiveness of the algorithm.

SECOND-ORDER STOCHASTIC VOLATILITY ASYMPTOTICS AND THE PRICING OF FOREIGN EXCHANGE DERIVATIVES

2020 ◽  
Vol 23 (03) ◽  
pp. 2050021
Author(s):  
TOMMASO PELLEGRINO
Keyword(s):  
Foreign Exchange ◽  
Order Approximation ◽  
Second Order ◽  
Option Prices ◽  
European Option ◽  
First Order ◽  
Singular Perturbation Methods ◽  
Asset Volatility ◽  
The One ◽  
Exchange Options

We consider models for the pricing of foreign exchange derivatives, where the underlying asset volatility as well as the one for the foreign exchange rate are stochastic. Under this framework, singular perturbation methods have been used to derive first-order approximations for European option prices. In this paper, based on a previous result for the calibration and pricing of single underlying options, we derive the second-order approximation pricing formula in the two-dimensional case and we apply it to the pricing of foreign exchange options.

Reflections on the concept of symmetry

2005 ◽  
Vol 13 (S2) ◽  
pp. 3-11 ◽  
Author(s):  
KUNO LORENZ
Keyword(s):  
Binary Relation ◽  
Second Order ◽  
The Other ◽  
First Order ◽  
Broken Symmetries ◽  
Other Hand ◽  
Logical Notion ◽  
The One ◽  
Ancient Usage

The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, ‘being symmetric’ in general usage is synonymous with ‘being harmonious’, and in technical usage, as in Euclid's Elements, it is synonymous with ‘commensurable’. Due to the second meaning, which is close to the etymology of συ´μμετρoς, ‘with measure’ has likewise to be read as ‘being [in] rational [ratios]’ and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.

Reliable and Failure-Free Workspaces for Motion Planning Algorithms for Parallel Manipulators Under Geometrical Uncertainties

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Hiparco L. Vieira ◽  
João V. C. Fontes ◽  
André T. Beck ◽  
Maíra M. da Silva
Keyword(s):  
Motion Planning ◽  
Parallel Manipulators ◽  
Monte Carlo Algorithm ◽  
Planning Algorithm ◽  
Dense Grid ◽  
Planning Strategies ◽  
Singular Configuration ◽  
The One ◽  
Failure Probabilities

Manufacturing tolerances and other uncertainties may play an important role in the performance of parallel manipulators since they can affect the distance to a singular configuration. Motion planning strategies for parallel manipulators under uncertainty require decision making approaches for classifying reliable regions within the workspace. In this paper, we address fail free and reliable motion planning for parallel manipulators. Failure is related to parallel kinematic singularities in the motion equations or to ill-conditioning of the Jacobian matrices. Monte Carlo algorithm is employed to compute failure probabilities for a dense grid of manipulator workspace configurations. The inverse condition number of the Jacobian matrix is used to compute the distance between each configuration and a singularity. For supporting motion planning strategies, not only failure maps are constructed but also reliable and failure-free workspaces are obtained. On the one hand, the reliable workspace is obtained by minimizing the failure probabilities subject to a minimal workspace area. Differently, a failure-free workspace is found by maximizing the workspace area subject to a probability of failure equal to zero. A 3RRR manipulator is used as a case study. For this case study, the usage of the reliable strategy can be useful for robustifying motion planning algorithm without a significant reduction of the reliable regions within the workspace.

scholarly journals Should a higher-order metaphysician believe in properties?

Synthese ◽  
2021 ◽  
Author(s):  
David Liggins
Keyword(s):  
Higher Order ◽  
Second Order ◽  
First Order ◽  
The One

AbstractIn this paper I take second order-quantification to be a sui generis form of quantification, irreducible to first-order quantification, and I examine the implications of doing so for the debate over the existence of properties. Nicholas K. Jones has argued that adding sui generis second-order quantification to our ideology is enough to establish that properties exist. I argue that Jones does not settle the question of whether there are properties because—like other ontological questions—it is first-order. Then I examine three of the main arguments for the existence of properties. I conclude that sui generis second-order quantification defeats the “one over many” argument and that, coupled with second-order predication, it also defeats the reference and quantification arguments.

scholarly journals On proving syntactic properties of CPS programs

1999 ◽  
Vol 6 (23) ◽  
Author(s):  
Olivier Danvy ◽  
Belmina Dzafic ◽  
Frank Pfenning
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Program Transformations ◽  
First Order ◽  
New Challenges ◽  
The One ◽  
Syntactic Properties

Higher-order program transformations raise new challenges for proving<br />properties of their output, since they resist traditional, first-order proof<br />techniques. In this work, we consider (1) the "one-pass" continuation-passing<br />style (CPS) transformation, which is second-order, and (2) the<br />occurrences of parameters of continuations in its output. To this end, we<br />specify the one-pass CPS transformation relationally and we use the proof<br />technique of logical relations.

scholarly journals Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

2021 ◽  
Vol 11 (21) ◽  
pp. 10245
Author(s):  
Arkadiusz Mielczarek ◽  
Ignacy Dulęba
Keyword(s):  
Motion Planning ◽  
Configuration Space ◽  
Algebraic Method ◽  
Nonholonomic Systems ◽  
Inverse Kinematic ◽  
General Purpose ◽  
Task Space ◽  
Local Motion ◽  
Planning Algorithm ◽  
Nonholonomic Motion Planning

In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.

Control and Motion Planning of a Nonholonomic Parallel Orienting Platform

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Janusz Jakubiak ◽  
Władyslaw Magiera ◽  
Krzysztof Tchoń
Keyword(s):  
Motion Planning ◽  
Translational Motion ◽  
Open Loop ◽  
Planning Algorithm ◽  
Parallel Platform ◽  
Practical Stabilization ◽  
Planning Problems ◽  
Form System ◽  
Loop Motion ◽  
Space Approach

An orienting platform is a mechanism which allows rotation of a spatial object without translational motion of that object. In this work, we study a parallel platform with one passive nonholonomic spherical joint and two series of spherical, actuated prismatic and universal joints (the platform is also known in literature as an (nS)-2SPU wrist). To solve the control and motion planning problems, an analytic approach is used. The design of practical stabilization and tracking algorithm is based on transverse functions and a method for motion planning respecting mechanical singularities is derived from endogenous configuration space approach. It is shown that the system is controllable and locally equivalent to the chained form system. Then, the stabilization, tracking, and motion planning algorithms are proposed. Results are verified with computer simulations. A combination of the open-loop motion planning algorithm and the closed-loop tracking provide a tool for designing a motion planning algorithm respecting mechanical singularities and robust to input disturbances.

The double function of the interpretant in Peirce’s theory of signs

Semiotica ◽  
2018 ◽  
Vol 2018 (225) ◽  
pp. 39-55
Author(s):  
Jimmy Aames
Keyword(s):  
Second Order ◽  
The Other ◽  
Logical Operation ◽  
Order Function ◽  
First Order ◽  
Formal Identity ◽  
Double Function ◽  
Hypostatic Abstraction ◽  
The One ◽  
Definition Of

AbstractThere seem to be two distinct aspects to the role played by the Interpretant in Peirce’s account of the sign relation. On the one hand, the Interpretant is said to establish the relation between the Sign and Object. That is, the Sign can “stand for” its Object, and thereby actually function as a Sign, only by virtue of its being interpreted as such by an Interpretant. On the other hand, the Interpretant is said to be “determined” by the Sign in such a way that it is thereby mediately determined by the Sign’s Object. How can we understand the relation between these two aspects of the Interpretant? This is the question with which this paper is concerned. I begin by drawing a distinction between what I call the first-order function and second-order function of the Interpretant, and illustrating this distinction using Peirce’s example of comparing the letters p and b in § 9 of the 1867 “On a New List of Categories.” I then show that this same distinction can be discerned in a significant passage in the second section of Peirce’s 1903 “A Syllabus of Certain Topics of Logic,” as well as in his early definition of the Interpretant in the “New List.” This double function of the Interpretant has been noted in the Peircean literature, specifically by Joseph Ransdell in his 1966 dissertation, and more recently by André De Tienne. However, an important aspect of what I call the second-order function of the Interpretant remains unclarified in Ransdell and De Tienne’s approaches, namely, its relation to the logical operation of hypostatic abstraction. I will show that the Interpretant, in its second-order function, plays a role formally identical in the sign process to the role played by hypostatic abstraction in Peirce’s demonstrations of the Reduction Thesis. This formal identity will afford us with a way of understanding the relation between the two aspects of the Interpretant in terms of hypostatic abstraction.

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