Time optimal trajectories for mobile robots with two independently driven wheels

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This paper addresses the problem of time-optional motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin's maximum principle (PMP), we formally demonstrate that all time optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the acceleration ... continued below

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Pages: (47 p)

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Reister, D.B. & Pin, F.G. March 1, 1992.

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Description

This paper addresses the problem of time-optional motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin's maximum principle (PMP), we formally demonstrate that all time optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the acceleration on each wheel is either at its upper or lower limit). The PMP, however, only provides necessary conditions for time optimality. To find the time optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this parameterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numerically that robot trajectories with three switch times (two on one wheel, one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving similar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters, and consist of subsets of trajectories with three switch times for the problem when the final orientation of the robot is not specified, and four switch times when a full final configuration is specified. We conclude with a description of the use of the method for trajectory planning for one of our robots.

Physical Description

Pages: (47 p)

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OSTI; NTIS; GPO Dep.

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  • Other: DE92010002
  • Report No.: ORNL/TM-12070
  • Report No.: CESAR--92/09
  • Grant Number: AC05-84OR21400
  • DOI: 10.2172/5541105 | External Link
  • Office of Scientific & Technical Information Report Number: 5541105
  • Archival Resource Key: ark:/67531/metadc1092903

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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Creation Date

  • March 1, 1992

Added to The UNT Digital Library

  • Feb. 10, 2018, 10:06 p.m.

Description Last Updated

  • March 5, 2018, 6:09 p.m.

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Reister, D.B. & Pin, F.G. Time optimal trajectories for mobile robots with two independently driven wheels, report, March 1, 1992; Tennessee. (digital.library.unt.edu/ark:/67531/metadc1092903/: accessed April 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.