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Optimal coverage trajectories for a UGV with tradeoffs for energy and time

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Abstract

Area coverage is a common task for an unmanned ground vehicle (UGV) that requires time and energy to complete. We have developed a novel cost function that can be used to optimally traverse a path that covers a region. The UGV model and cost function are developed theoretically and verified experimentally. Our cost function weights force inputs, area covered and motor efficiency to create an optimal trajectory. This trajectory is constrained to follow a coverage path described in the literature. The path is modified based on the cost function by replacing turn-in-place maneuvers by moving turns. Tradeoffs are presented for three cases: (1) drive motor efficiency is not considered, (2) the motors are most efficient at the maximum velocity, and (3) the motors are most efficient below the maximum velocity. Optimality tradeoffs include the time required to cover the region, and the energy required to complete the trajectory. Experimental results using an iRobot Packbot are presented.

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Abbreviations

\(I_{l,r}\) :

Motor currents (left and right)

\( v_{track}\) :

Track velocity

\(K_m\) :

Motor constant

\(K_r\) :

Gear ratio

\(\mathbf q \) :

UGV state

\((x_R,y_R)\) :

UGV positions

\(v\) :

UGV velocity

\(\theta \) :

UGV heading

\(\omega \) :

UGV turn rate

\(u_{r,l}\) :

UGV track force inputs

\(u^*_{max}\) :

UGV maximum input

\(v_{max}\) :

UGV maximum velocity

\(K_{0,1,2}\) :

Cost function gains

\(\mathrm{meas }(\varPsi (t))\) :

Fraction of area uncovered

\({\text{ E }}(\omega _{motor})\) :

Motor efficiency penalty

\({\mathrm{eff}}(\omega _{motor}^{r,l})\) :

Motor efficiency

\(v_{_{{ eff }}}\) :

UGV velocity at maximum efficiency

\(s\) :

Straight line UGV position

\(\fancyscript{H}\) :

Hamiltonian Function

\(\mathbf p \) :

Costate variables

\(\theta \) :

Turn in place UGV heading

\(\tau \) :

Turn in place UGV input

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Acknowledgments

This research was supported in part by the Automotive Research Center (ARC) at the University of Michigan, with funding from government contract DoD-DoA W56H2V-04-2-0001 through the US Army Tank Automotive Research, Development, and Engineering Center

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Authors and Affiliations

  1. Electrical Engineering: Systems Department, University of Michigan, Ann Arbor, MI, USA

    John A. Broderick

  2. Mechanical Engineering Department, University of Michigan, Ann Arbor, MI, USA

    Dawn M. Tilbury

  3. Aerospace Engineering Department, University of Michigan, Ann Arbor, MI, USA

    Ella M. Atkins

Authors
  1. John A. Broderick
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  2. Dawn M. Tilbury
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  3. Ella M. Atkins
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Correspondence to John A. Broderick.

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Broderick, J.A., Tilbury, D.M. & Atkins, E.M. Optimal coverage trajectories for a UGV with tradeoffs for energy and time. Auton Robot 36, 257–271 (2014). https://doi.org/10.1007/s10514-013-9348-x

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