Communications in Analysis and Mechanics最新文献

Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces 伪欧几里德空间中超二次曲面的纯滚动运动

Communications in Analysis and Mechanics Pub Date : 2022-01-12 DOI: 10.3934/jgm.2021033

André Marques, Fátima Silva Leite

{"title":"Pure rolling motion of hyperquadrics in pseudo-Euclidean spaces","authors":"André Marques, Fátima Silva Leite","doi":"10.3934/jgm.2021033","DOIUrl":"https://doi.org/10.3934/jgm.2021033","url":null,"abstract":"<p style='text-indent:20px;'>This paper is devoted to rolling motions of one manifold over another of equal dimension, subject to the nonholonomic constraints of no-slip and no-twist, assuming that these motions occur inside a pseudo-Euclidean space. We first introduce a definition of rolling map adjusted to this situation, which generalizes the classical definition of Sharpe [<xref ref-type=\"bibr\" r>26</xref>] for submanifolds of an Euclidean space. We also prove some important properties of these rolling maps. After presenting the general framework, we analyse the particular rolling of hyperquadrics embedded in pseudo-Euclidean spaces. The central topic is the rolling of a pseudo-hyperbolic space over the affine space associated with its tangent space at a point. We derive the kinematic equations, as well as the corresponding explicit solutions for two specific cases, and prove the existence of a rolling map along any curve in that rolling space. Rolling of a pseudo-hyperbolic space on another and rolling of pseudo-spheres are equally treated. Finally, for the central theme, we write the kinematic equations as a control system evolving on a certain Lie group and prove its controllability. The choice of the controls corresponds to the choice of a rolling curve.</p>","PeriodicalId":501380,"journal":{"name":"Communications in Analysis and Mechanics","volume":"257 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138523158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Efficient geometric linearization of moving-base rigid robot dynamics 运动基座刚性机器人动力学的有效几何线性化

Communications in Analysis and Mechanics Pub Date : 2022-01-01 DOI: 10.3934/jgm.2022009

Martijn Bos,Silvio Traversaro,Daniele Pucci,Alessandro Saccon

{"title":"Efficient geometric linearization of moving-base rigid robot dynamics","authors":"Martijn Bos,Silvio Traversaro,Daniele Pucci,Alessandro Saccon","doi":"10.3934/jgm.2022009","DOIUrl":"https://doi.org/10.3934/jgm.2022009","url":null,"abstract":"<p style='text-indent:20px;'>The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state estimation. Contrary to the case of fixed based manipulators with prismatic or revolute joints, the state space of moving-base robotic systems such as humanoids, quadruped robots, or aerial manipulators cannot be globally parametrized by a finite number of independent coordinates. This impossibility is a direct consequence of the fact that the state of these systems includes the system's global orientation, formally described as an element of the special orthogonal group SO(3). As a consequence, obtaining the linearization of the equations of motion for these systems is typically resolved, from a practical perspective, by locally parameterizing the system's attitude by means of, e.g., Euler or Cardan angles. This has the drawback, however, of introducing artificial parameterization singularities and extra derivative computations. In this contribution, we show that it is actually possible to define a notion of linearization that does not require the use of a local parameterization for the system's orientation, obtaining a mathematically elegant, recursive, and singularity-free linearization for moving-based robot systems. Recursiveness, in particular, is obtained by proposing a nontrivial modification of existing recursive algorithms to allow for computations of the geometric derivatives of the inverse dynamics and the inverse of the mass matrix of the robotic system. The correctness of the proposed algorithm is validated by means of a numerical comparison with the result obtained via geometric finite difference.</p>","PeriodicalId":501380,"journal":{"name":"Communications in Analysis and Mechanics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

From Schouten to Mackenzie: Notes on brackets 从舒滕到麦肯齐:括号注释

Communications in Analysis and Mechanics Pub Date : 2021-07-15 DOI: 10.3934/jgm.2021013

Yvette Kosmann-Schwarzbach

引用次数: 0

Erratum: Constraint algorithm for singular field theories in the begin{document}$ k $end{document}-cosymplectic framework Erratum: Constraint algorithm for singular field theories in the begin{document}$ k $end{document}-cosymplectic framework

Communications in Analysis and Mechanics Pub Date : 2021-05-12 DOI: 10.3934/jgm.2021007

Xavier Gràcia, Xavier Rivas, Narciso Román-Roy

引用次数: 0