Efficient Cartesian Path Approximation for Robots Using Trigonometric Splines

Daniel J. Simon; Can Isik

doi:10.1109/ACC.1994.752373

Efficient Cartesian Path Approximation for Robots Using Trigonometric Splines

Daniel J. Simon
, Can Isik

Syracuse University

Research output: Contribution to journal › Article › peer-review

Abstract

A smooth approximation of a desired robot path can be realized by interpolating a sequence of joint-space knots with a trigonometric spline. In this paper we derive the computational effort required for the formulation of trigonometric splines and show how real-time obstacle avoidance can be implemented. The required computational expense is calculated and compared to that of algebraic splines. In addition, we demonstrate analytically that the Cartesian path error resulting from the use of trigonometric splines is inversely proportional to the number of knots if certain assumptions are satisfied. We then verify this result numerically, and extend the result numerically to cases where the given assumptions are not satisfied.

Original language	American English
Journal	American Control Conference
Volume	2
DOIs	https://doi.org/10.1109/ACC.1994.752373
State	Published - Jun 1 1994

Keywords

Computational effort
Efficient Cartesian path approximation
Interpolation
Joint-space knots
Real-time obstacle avoidance
Robots
Smooth approximation
Trigonometric splines

Disciplines

Electrical and Computer Engineering
Robotics

Access to Document

10.1109/ACC.1994.752373License: CC BY

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=752373

Cite this

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title = "Efficient Cartesian Path Approximation for Robots Using Trigonometric Splines",

abstract = " A smooth approximation of a desired robot path can be realized by interpolating a sequence of joint-space knots with a trigonometric spline. In this paper we derive the computational effort required for the formulation of trigonometric splines and show how real-time obstacle avoidance can be implemented. The required computational expense is calculated and compared to that of algebraic splines. In addition, we demonstrate analytically that the Cartesian path error resulting from the use of trigonometric splines is inversely proportional to the number of knots if certain assumptions are satisfied. We then verify this result numerically, and extend the result numerically to cases where the given assumptions are not satisfied.",

keywords = "Computational effort, Efficient Cartesian path approximation, Interpolation, Joint-space knots, Real-time obstacle avoidance, Robots, Smooth approximation, Trigonometric splines",

author = "Simon, \{Daniel J.\} and Can Isik",

note = "D. Simon and C. Isik. (1994). Efficient Cartesian Path Approximation for Robots Using Trigonometric Splines. American Control Conference, 1752-1756, doi: 10.1109/ACC.1994.752373.",

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doi = "10.1109/ACC.1994.752373",

language = "American English",

volume = "2",

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AU - Isik, Can

N1 - D. Simon and C. Isik. (1994). Efficient Cartesian Path Approximation for Robots Using Trigonometric Splines. American Control Conference, 1752-1756, doi: 10.1109/ACC.1994.752373.

PY - 1994/6/1

Y1 - 1994/6/1

N2 - A smooth approximation of a desired robot path can be realized by interpolating a sequence of joint-space knots with a trigonometric spline. In this paper we derive the computational effort required for the formulation of trigonometric splines and show how real-time obstacle avoidance can be implemented. The required computational expense is calculated and compared to that of algebraic splines. In addition, we demonstrate analytically that the Cartesian path error resulting from the use of trigonometric splines is inversely proportional to the number of knots if certain assumptions are satisfied. We then verify this result numerically, and extend the result numerically to cases where the given assumptions are not satisfied.

AB - A smooth approximation of a desired robot path can be realized by interpolating a sequence of joint-space knots with a trigonometric spline. In this paper we derive the computational effort required for the formulation of trigonometric splines and show how real-time obstacle avoidance can be implemented. The required computational expense is calculated and compared to that of algebraic splines. In addition, we demonstrate analytically that the Cartesian path error resulting from the use of trigonometric splines is inversely proportional to the number of knots if certain assumptions are satisfied. We then verify this result numerically, and extend the result numerically to cases where the given assumptions are not satisfied.

KW - Computational effort

KW - Efficient Cartesian path approximation

KW - Interpolation

KW - Joint-space knots

KW - Real-time obstacle avoidance

KW - Robots

KW - Smooth approximation

KW - Trigonometric splines

UR - https://engagedscholarship.csuohio.edu/enece_facpub/169

UR - http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=752373

U2 - 10.1109/ACC.1994.752373

DO - 10.1109/ACC.1994.752373

M3 - Article

VL - 2

JO - American Control Conference

JF - American Control Conference

ER -

Efficient Cartesian Path Approximation for Robots Using Trigonometric Splines

Abstract

Keywords

Disciplines

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