From Obstacle Avoidance To Motion Learning Using Local Rotation of Dynamical Systems Lukas Huber1

2025-05-06 0 0 1.74MB 4 页 10玖币

侵权投诉

From Obstacle Avoidance To Motion Learning

Using Local Rotation of Dynamical Systems

Lukas Huber1

Abstract— In robotics motion is often described from an

external perspective, i.e., we give information on the obstacle

motion in a mathematical manner with respect to a speciﬁc

(often inertial) reference frame. In the current work, we propose

to describe the robotic motion with respect to the robot itself.

Similar to how we give instructions to each other (“go straight,

and then after xxx meters move left, and then turn left.”), we

give the instructions to a robot as a relative rotation.

We ﬁrst introduce an obstacle avoidance framework that allows

avoiding star-shaped obstacles while trying to stay close to an

initial (linear or nonlinear) dynamical system. The framework

of the local rotation is extended to motion learning. Automated

clustering deﬁnes regions of local stability, for which the precise

dynamics are individually learned.

The framework has been applied to the LASA-handwriting

dataset and shows promising results.

I. INTRODUCTION

Motion learning and programming by demonstration have

seen large development in recent years, thanks to progress

in machine learning algorithms, improved computational

capacities but also the large availability of data. In this work,

we introduce a framework that allows the combination of

the two approaches. This not only allows the exploitation of

synergies between learning and avoiding but also allows the

division of the task into globally learned motion and local

obstacle avoidance.

A. Properties

The learned dynamics have the following properties:

•continuously differentiable (C1smooth).

•globally asymptotically stable.

•the learning can be applied to any (non-crossing) tra-

jectory. Speciﬁcally, motions that lead away from the

attractor in the radial direction, i.e.,

hf(ξ),ξ−ξai/(kf(ξ)kkξ−ξak) = (−1)(1)

and spiraling motion

Additional advantages of the systems are:

•The motion can be constrained to a region of inﬂuence

using a radius Rkmeans to ensure proximity to the initial

data points, i.e., creating an invariant set around the

known environment.

•The motion learning can be combined with avoidance

algorithms to ensure convergence towards the attractor

around (locally star-shaped) obstacles for the constraint

region.

Fig. 1: Robotic arm avoiding obstacles while following a previously

learned dynamical system [1]

II. LITERATURE

A popular method of learning from demonstration is

SEDS [2]. It ensures stability by using a quadratic Lyapunov

function, this comes with the cost of low accuracy for non-

monotonic trajectories (temporarily moving away from the

attractor). A parametrized quadratic Lyapunov function offer

more ﬂexibility, but still struggle to approximate non-linear

trajectories [3].

More complex Lyapunov functions can be automatically

learned to ensure the stability of the ﬁnal control [4]. This

has been further extended to additionally learn the control

parameters of the motion [5], [6]. A weighted sum of

asymmetric quadratic functions (WSAQF) is used to obtain

the ﬁnal Lyapunov candidate, which limits the motion to not

be able to move in radial direction away from the attractor.

Diffeomorphic matching of an initial linear trajectory with

the learned trajectory (highly nonlinear) [7], [8]. However,

the work cannot give any guarantees on the convergence of

the matching.

Dynamic movement primitives introduce time-dependent

parameters which ensure the convergence in ﬁnite time

towards the goal [9]. However, this leads to motion increas-

ingly deviating from the learned motion with increasing time.

III. OBSTACLE AVOIDANCE THROUGH ROTATION

A. Preliminaries

We restate concepts developed in [1], [10]. The most direct

dynamics towards the attractor is a linear dynamical system

of the form:

f(ξ) = −k(ξ−ξa)(2)

where k∈Ris a scaling parameter.

Real-time obstacle avoidance is obtained by applying a

dynamic modulation matrix to a dynamical system f(ξ):

ξ=M(ξ)f(ξ)with M(ξ) = E(ξ)D(ξ)E(ξ)−1(3)

arXiv:2210.14417v1 [cs.RO] 26 Oct 2022

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

FromObstacleAvoidanceToMotionLearningUsingLocalRotationofDynamicalSystemsLukasHuber1AbstractInroboticsmotionisoftendescribedfromanexternalperspective,i.e.,wegiveinformationontheobstaclemotioninamathematicalmannerwithrespecttoaspecic(ofteninertial)referenceframe.Inthecurrentwork,weproposetodescribe...

展开>> 收起<<

From Obstacle Avoidance To Motion Learning Using Local Rotation of Dynamical Systems Lukas Huber1.pdf

共4页,预览1页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

From Obstacle Avoidance To Motion Learning Using Local Rotation of Dynamical Systems Lukas Huber1

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: