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Motion planning of a snake-like robot using an optimized harmonic potential field

  • Research Article
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Paladyn

Abstract

Snake-like robots have gained popularity in the last three decades for their ability to utilize several gaits in order to navigate through different terrains. They are analogous in morphology to snakes, tentacles, and elephant trunks. We propose a novel method of navigating a snake-like robot based on the Harmonic Field with Optimized Boundary Conditions (HFOBC) and a boundary following algorithm. We apply the HFOBC navigation function using a number of fictitious charges equally spaced on each link. These charges actively follow the potential field towards the target. Futhermore, a generalized mathematical model for an n-link snake-like robot based on Lagrange formulation has also been proposed in this paper.

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Abbreviations

\( \vec p_i \) :

A vector from the robot to the obstacle O i

\( \vec p_\beta \) :

A vector from the robot to the target β

\( U_i (\vec p_i ) \) :

A repelling potential field due to the obstacle i

\( U_\beta (\vec p_\beta ) \) :

Attractive potential field due to target β

\( \varphi (\vec p) \) :

Harmonic potential field value for vector \( \vec p \)

L :

Minimum distance from the robot to the closest obstacle

R :

Safety distance

\( \vec n \) :

A unit vector perpendicular to the boundary in the direction of the robot

\( \vec \tau \) :

A unit vector tangential to the boundary in the direction of the negative gradient of the potential field

N i :

Number of charges on link i in the snake robot

(x i , y i ):

Position of the center of gravity of the link i

(x 0, y 0):

Position of the first charge of the first link

m i :

Mass of link i

l i :

Length of link i

θ i :

Angle of link i with the global x-axis

ψ i :

Angle between link i and link i − 1

T :

Kinetic energy

V :

Potential energy

k :

Torsional spring constant

M :

Inertia matrix

C :

Coriolis terms vector

G :

Potential energy vector

q i :

Generalized coordinate

Q a :

Generalized forces vector due to actuators

Q c :

Generalized forces vector due to charges’ forces

Z i :

Position of the beginning of link i

\( \vec r_j^i \) :

Position of charge j on link i

\( \delta \vec r_j^i \) :

Virtual displacement of the charge j on the link i

δ W :

Virtual work

\( \vec F_j^i \) :

The potential field force acting on charge j on the link i

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Authors and Affiliations

  1. Automated Precision, Inc., Rockville, MD, 20850, USA

    Samer Charifa

  2. Department of Electrical and Computer, Engineering North Carolina Agricultural and Technical State University Greensboro, Greensboro, NC, 27411, USA

    Marwan Bikdash

Authors
  1. Samer Charifa
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  2. Marwan Bikdash
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Correspondence to Samer Charifa.

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Charifa, S., Bikdash, M. Motion planning of a snake-like robot using an optimized harmonic potential field. Paladyn 1, 187–197 (2010). https://doi.org/10.2478/s13230-011-0005-9

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