 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12788 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8028
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| In English (Mech. Solids): | | 4760 |
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| E.A. Mikishanina, "Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem," Mech. Solids. 59 (1), 127-141 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
1 |
Pages |
127-141 |
| DOI |
10.1134/S0025654423601192 |
| Title |
Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem |
| Author(s) |
E.A. Mikishanina (Ulianov Chuvash State University, Cheboksary, 428015 Russia, evaeva_84@mail.ru) |
| Abstract |
We consider the problem of controlling a spherical robot with a pendulum actuator rolling
on a platform that is capable of moving translationally in the horizontal plane of absolute space.
The spherical robot is subject to holonomic and nonholonomic constraints. Some point target moves
at the level of the geometric center of the spherical robot and does not touch the moving platform itself.
The motion program that allows the spherical robot to pursue a target is specified through two servoconstraints. The robot can follow a target from any position and with any initial conditions. Two ways
to control this system in absolute space are proposed: by controlling the forced motion of the platform
(the pendulum oscillates freely) and by controlling the torque of the pendulum (the platform is stationary or oscillates inconsistently with the spherical robot). The equations of motion of the system are
constructed. In the case of free oscillations of the pendulum, the system of equations of motion has
first integrals and, if necessary, can be reduced to a fixed level of these integrals. When a spherical
robot moves in a straight line, for a system reduced to the level of integrals, phase curves, graphs of the
distance from the geometric center of the spherical robot to the target, the trajectory of the selected
platform point when controlling the platform, and the square of the control torque when controlling
the pendulum actuator are constructed. When the robot moves along a curved path, integration is carried out in the original variables. Graphs of the squares of the angular velocity of the pendulum and
the spherical robot itself are constructed, as well as the trajectory of the robot’s motion in absolute
space and on a moving platform. Numerical experiments were performed in the Maple software package. |
| Keywords |
control, nonholonomic system, spherical robot, pendulum actuator, moving platform, servo-constraint, pursuit |
| Received |
17 May 2023 | Revised |
14 July 2023 | Accepted |
16 July 2023 |
| Link to Fulltext |
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