Locomotion Principles for Mobile Robotic Systems - ScienceDirect

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ScienceDirect Procedia Computer Science 103 (2017) 613 – 617

XIIth International Symposium «Intelligent Systems», INTELS’16, 5-7 October 2016, Moscow, Russia

Locomotion Principles for Mobile Robotic Systems F.L. Chernousko* Institute for Problems in Mechanics, Russian Academy of Sciences Moscow Institute of Physics and Technology, Moscow, Russia

Abstract Locomotion of mobile robots over surfaces and in various media can be based upon different principles. The most widespread types of locomotion are motions using special outer devices like wheels, legs, tracks, and propellers. Also, locomotion of multibody systems can be based upon periodic change of configuration of the system. In the paper, such types of progressive motions for multibody robotic systems are discussed and illustrated. Some of these types of locomotion are similar to those used by living organisms: animals, fish, and insects. Other types have no obvious analogs in the nature. The following locomotion principles are discussed. © 2017 2017The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the XIIth International Symposium «Intelligent Systems». Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” Keywords: locomotion; multi-body system

1. Introduction Locomotion of mobile robots over surfaces and in various media can be based upon different principles. The most wide-spread types of locomotion are motions using special outer devices like wheels, legs, tracks, and propellers. Also, locomotion of multibody systems can be based upon periodic change of configuration of the moving system. In the paper, such types of progressive motions caused by the change of configuration of multibody systems are discussed. Some of these types of locomotion are similar to those used by living organisms: animals, fish, and insects. Other types have no direct analogs in the nature.

* Corresponding author.. E-mail address: [email protected]

1877-0509 © 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the XIIth International Symposium “Intelligent Systems” doi:10.1016/j.procs.2017.01.081

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F.L. Chernousko / Procedia Computer Science 103 (2017) 613 – 617

For locomotion types under consideration, it is important to find the most efficient modes of motion. To this end, a number of optimization problems are solved. Optimal values of system parameters and optimal controls of actuators are obtained that correspond to the maximum average locomotion speed and/or minimum energy spent per unit path. 2. Snake-like motions Snake-like motions always caused interest in biomechanics1 and robotics2. Consider a multilink system (Fig. 1) lying on a horizontal plane and consisting of straight rigid links connected consecutively by cylindrical joints where m actuators are placed. Denote by li the length of the i -th link, by i the mass of the i -th joint, and by M i the torque created by the i -th actuator. For simplicity, we neglect the masses of links compared to those of joints. The system is subjected to the dry friction forces obeying Coulomb′s law: kmi gv i / v i , if v i z 0, F i d kmi g , if v i 0. Fi

(1)

Here, k is the coefficient of friction and g is gravity acceleration

Fig. 1. Multilink system

It is shown that the multink system consisting of several links can move along a plane by means of special alternation of slow and fast phases of motion 3,4. In slow phases, only the end links move, whereas all other links stay at rest. In fast phases, all links are in motion, and the torques M i created by actuators are large enough: M i >> km gl , m

max mi ,

l

i

max li .

(2)

i

Under condition (2), the friction forces can be neglected during fast phases. It is shown that, using slow and fast phases, the multilink systems can perform longitudinal and lateral motions, rotations, and move from the initial position and configuration to any prescribed position and configuration in the plane3,4. In other words, these systems are completely controllable. The optimal geometrical and mechanical parameters as well as the parameters of the slow and fast phases of motion are found that correspond to the maximum average locomotion speed5. Minimization of the energy consumption is also investigated. 3. Quasi-static motions In quasi-static motions of multilink mechanisms, only slow phases occur in which all velocities and accelerations are sufficiently small. Thus, quasi-static locomotion is, in fact, a sequence of equilibrium positions where the torques produced by the actuators are counterbalanced by friction forces. A two-link system cannot move in a quasi-static way


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beyond a certain circle. For a three-link system, quasi-static motions are possible only under certain conditions. It is shown6,7 that a multilink system consisting of N equal links can perform wavelike locomotion, if N t 5 . In this motion, a wave composed of three or four moving links travels along the multilink system, whereas all other links stay at rest. As a result, the whole chain of links performs a longitudinal motion along itself. Two-dimensional quasi-static motion along a horizontal plane of a system consisting of three point masses is investigated8. Each pair of masses interact with each other by means of control forces (attraction or repulsion) directed along the lines connecting these masses. It is shown that the system is controllable, i.e., it can move from any initial position and configuration to any terminal position and configuration, if and only if the masses satisfy the triangle inequality: mi m j t mk ,

i, j , k {1, 2, 3} .

4. Motions in fluids Mobile robots imitating swimming of fish were discussed in many papers, e.g.9-11. In our works, we consider optimal motions in fluids for multibody systems that consist of a main body and several links attached to it by cylindrical joints. A fish-like system has one link (a tail) attached to the main body, whereas a frog-like system has a pair of symmetric legs that consist of two links each (Fig. 2). The actuators installed at the joints make the links to perform periodic oscillations about the axis of symmetry of the system. All elements of the system are subjected to the resistance forces that are proportional to the squared velocity of the element and directed against this velocity. The analysis of the equations of motion shows that both the fish-like and frog-like systems can move progressively along their axes. Their average velocities are evaluated that depend on the system parameters and periodic relative motions of the attached links.

Fig. 2. Fish-like and frog-like systems.

Optimal relative motions corresponding to the maximum average velocity are found12-14. These optimal motions have the following characteristic qualitative property: the angular velocities of deflection of the links from the axis of symmetry are smaller than the angular velocities of their return to the axis. This property is confirmed by observations of swimming creatures. Among other mechanical models of locomotion in fluids are systems imitating rowing boats15 and a chain of interacting bodies where the distances between them change during the progressive motion. 5. Systems containing internal masses Consider a system consisting of a main body (a container) of mass M and an internal body of mass m that can move inside the main body (Fig. 3). The main body moves in an outer medium and is subjected to the resistance force depending on its velocity. This force can be dry friction described by (1), linear or quadratic resistance, either isotropic or anisotropic (dependent on the direction of motion). The internal mass is equipped with an actuator and moves periodically within the main body but does not interact with the outer medium. This system as a whole can move progressively with a velocity changing periodically.

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Fig. 3. Systems containing internal masses.

Mobile robots whose locomotion is based upon the motion of internal masses are sometimes called vibro-robots or capsubots; they have no direct analogs in the nature. Such robots are used for precise positioning16-20 and motion inside tubes21. Since such robots have no outer devices and can be made hermetic, they can be useful for motion in vulnerable, complicated, and hazardous environment, in pipelines and also in medical applications. In our paper, we have studied the dynamics of robotic systems containing moving internal masses, evaluated the average locomotion speed depending on the system parameters, and obtained the optimal motions that correspond to the maximum speed22-25. The results of experiments confirm the theoretical estimates and conclusions26,27. 6. Conclusions Non-traditional types of mobile robots that have no wheels, legs, tracks, and propellers and whose locomotion is based upon periodic change of their configuration are examined. Dynamics and optimal modes of locomotion for these systems are investigated. Acknowledgements The work was supported by the Russian Science Foundation, Project 14-11-00298. References 1. Gray J. Animal Locomotion. New York: Norton; 1968. 2. Hirose S. Biologically Inspired Robots: Snake-Like Locomotors and Manipulators. Oxford: Oxford University Press; 1993. 3. Chernousko F.L. The motion of a multilink system along a horizontal plane. Journal of Applied Mathematics and Mechanics 2000 64 1, p. 5-15. 4. Chernousko F.L. Controllable motions of a two-link mechanism along a horizontal plane. Journal of Applied Mathematics and Mechanics 2001 65 4, p. 565-577. 5. Chernousko F.L. Snake-like locomotions of multilink mechanisms. Journal of Vibration and Control 2003 9 1-2, p. 235-256. 6. Chernousko F.L. The wavelike motion of a multilink system on a horizontal plane. Journal of Applied Mathematics and Mechanics 2000 64 4, p. 497-508. 7. Chernousko F.L. Modelling of snake-like locomotion. Journal of Applied Mathematics and Computation 2005 164 2,p. 415-434. 8. Borisenko I., Chernousko F., Figurina T. Quasi-static motions of a three-body mechanism along a plane. Advances on theory and practice of robots and manipulators. Proceedings of ROMANSY 2014 XX CISM-IFTOMM Symposium. Cham: Springer; 2014, p. 175- 179. 9. Lighthill J. Mathematical Biofluiddynamics. Philadelphia: SIAM; 1975. 10. Blake R.W. Fish Locomotion. Cambridge: Cambridge University Press; 1983. 11. Colgate J.E., Lynch K.M. Mechanics and control of swimming: a review. IEEE, J. Oceanic Engng, 2004 29, p. 660-673. 12. Chernousko F.L. Optimal motion of a two-body system in a resistive medium. Journal of Optimization Theory and Applications 2010 147 2, p. 278-297. 13. Chernousko F.L. Motion of oscillating two-link system in fluid. IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design. Springer, Dordrecht, 2013. P. 109-121. 14. Karmanov S.P., Chernousko F.L. Modeling of Breaststroke Swimming. Doklady Physics 2014 59 2,p. 103-106. 15. Karmanov S.P., Chernousko F.L. An Elementary Model of the Rowing Process. Doklady Physics 2015 60 3, p. 140-144. 16. Breguet J.-M., Clavel R. Stick and slip actuators: design, control, performances and applications. Proceeding of International Symposium Micromechatronics and Human Science (MHS), New York: IEEE, 1998. p. 89-95. 17. Schmoeckel E., Worn H. Remotely controllable mobile microrobots acting as nano positioners and intelligent tweezers in scanning electron microscopes (SEMs). Proceedings of International Conference Robotics and Automation, 2001, New York: IEEE. p. 3903-3913.


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18. Lampert P., Vakebtutu A., Lagrange B., De Lit P., Delchambre A. Design and performances of a one-degree-of-freedom guided nano-actuator. Robot. Comput. Integr. Manuf., 2003 19 1-2, p. 89-98. 19. Vartholomeos P., Papadopoulos E. Dynamics, design and simulation of a novel micro-robotic platform employing vibration microactuators. Transactions ASME. J. Dyn. Syst. Meas. Control 2006 128 1, p. 122-133. 20. Zimmermann K., Zeidis I., Behn C. Mechanics of Terrestrial Locomotion. Berlin: Springer; 2009. 21. Gradetsky V., Solovtsov V., Kniazkov M., Rizzotto G., Amato P. Modular design of electro-magnetic mechatronic microrobots. Proceedings of 6th International Conference Climbing and Walking Robots CLAWAR,2003, p. 651-658. 22. Chernousko F.L. Analysis and optimization of the motion of a body controlled by a movable internal mass. Journal of Applied Mathematics and Mechanics 2006 70 6, p. 915-941. 23. Chernousko F.L. Dynamics of a body controlled by internal motions. Proceedings of IUTAM Symposium Dynamics and Control of Nonlinear Systems with Uncertainty, 2007. Dordrecht: Springer, p. 227-236. 24. Chernousko F.L. The optimal periodic motions of a two-mass system in resistant medium. Journal of Applied Mathematics and Mechanics 2008 72 2,p. 116-125. 25. Chernousko F.L. Dynamics and optimization of multibody systems in the presence of dry friction. Constructive Nonsmooth Analysis and Related Topics. New York: Springer, 2014, p. 71-100. 26. Li H., Furuta K., Chernousko F.L. A pendulum-driven cart via internal force and static friction. Proceedings of International Conference “Physics and Control, St. Petersburg, Russia, 2005, p. 15-17. 27. Li H., Furuta K., Chernousko F.L. Motion generation of the Capsubot using internal force and static friction. Proceeding of the 45th IEEE Conference Decision and Control, San Diego, USA, 2006, p. 6575-6580.