# Limited range spatial load balancing in non-convex environments using sampling-based motion planners

## Abstract

This paper analyzes the limited range, spatial load balancing problem for agents deployed in non-convex environments and subject to differential constraints which restricts how the agents can move. First, the (unlimited range) spatial load balancing problem is introduced and the minimization problem with area constraints is defined. Then, to extend the problem for limited ranges, two cost functions and a sub-partition are defined. The problems are then analyzed and the results prove the existence of a partition that satisfies the area constraints. The non-convex environment makes the problem difficult to solve in continuous-space. Therefore, a probabilistic roadmap is used to approximate agents’ cells via a graph. A distributed algorithm is proven to converge to an approximate solution. Lastly, the convergence of the algorithm is shown in simulation.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of California, San Diego, La Jolla, CA (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1459630

- Report Number(s):
- LA-UR-16-27817

Journal ID: ISSN 0929-5593

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Autonomous Robots

- Additional Journal Information:
- Journal Volume: 42; Journal Issue: 8; Journal ID: ISSN 0929-5593

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Motion Planning; Coverage; Load Balancing; Robotics

### Citation Formats

```
Boardman, Beth Leigh, Harden, Troy Anthony, and Martinez, Sonia. Limited range spatial load balancing in non-convex environments using sampling-based motion planners. United States: N. p., 2018.
Web. doi:10.1007/s10514-018-9713-x.
```

```
Boardman, Beth Leigh, Harden, Troy Anthony, & Martinez, Sonia. Limited range spatial load balancing in non-convex environments using sampling-based motion planners. United States. doi:10.1007/s10514-018-9713-x.
```

```
Boardman, Beth Leigh, Harden, Troy Anthony, and Martinez, Sonia. Mon .
"Limited range spatial load balancing in non-convex environments using sampling-based motion planners". United States. doi:10.1007/s10514-018-9713-x. https://www.osti.gov/servlets/purl/1459630.
```

```
@article{osti_1459630,
```

title = {Limited range spatial load balancing in non-convex environments using sampling-based motion planners},

author = {Boardman, Beth Leigh and Harden, Troy Anthony and Martinez, Sonia},

abstractNote = {This paper analyzes the limited range, spatial load balancing problem for agents deployed in non-convex environments and subject to differential constraints which restricts how the agents can move. First, the (unlimited range) spatial load balancing problem is introduced and the minimization problem with area constraints is defined. Then, to extend the problem for limited ranges, two cost functions and a sub-partition are defined. The problems are then analyzed and the results prove the existence of a partition that satisfies the area constraints. The non-convex environment makes the problem difficult to solve in continuous-space. Therefore, a probabilistic roadmap is used to approximate agents’ cells via a graph. A distributed algorithm is proven to converge to an approximate solution. Lastly, the convergence of the algorithm is shown in simulation.},

doi = {10.1007/s10514-018-9713-x},

journal = {Autonomous Robots},

number = 8,

volume = 42,

place = {United States},

year = {2018},

month = {2}

}

#### Figures / Tables:

_{$i$}.

Works referenced in this record:

##
Sampling-based algorithms for optimal motion planning

journal, June 2011

- Karaman, Sertac; Frazzoli, Emilio
- The International Journal of Robotics Research, Vol. 30, Issue 7

##
A note on two problems in connexion with graphs

journal, December 1959

- Dijkstra, E. W.
- Numerische Mathematik, Vol. 1, Issue 1

##
Least squares quantization in PCM

journal, March 1982

- Lloyd, S.
- IEEE Transactions on Information Theory, Vol. 28, Issue 2

##
Multi-robot coverage and exploration on Riemannian manifolds with boundaries

journal, October 2013

- Bhattacharya, Subhrajit; Ghrist, Robert; Kumar, Vijay
- The International Journal of Robotics Research, Vol. 33, Issue 1

##
Deployment algorithms for a power-constrained mobile sensor network

journal, May 2010

- Kwok, Andrew; Martínez, Sonia
- International Journal of Robust and Nonlinear Control, Vol. 20, Issue 7

##
Distributed Algorithms for Environment Partitioning in Mobile Robotic Networks

journal, August 2011

- Pavone, Marco; Arsie, Alessandro; Frazzoli, Emilio
- IEEE Transactions on Automatic Control, Vol. 56, Issue 8

##
Distributed Coverage Control and Data Collection With Mobile Sensor Networks

journal, October 2011

- Zhong, Minyi; Cassandras, Christos G.
- IEEE Transactions on Automatic Control, Vol. 56, Issue 10

##
Distributed coverage control for concave areas by a heterogeneous Robot–Swarm with visibility sensing constraints

journal, March 2015

- Kantaros, Yiannis; Thanou, Michalis; Tzes, Anthony
- Automatica, Vol. 53

##
Coverage Optimization and Spatial Load Balancing by Robotic Sensor Networks

journal, March 2010

- Cortes, J.
- IEEE Transactions on Automatic Control, Vol. 55, Issue 3

##
Distributed Deployment Algorithms for Improved Coverage in a Network of Wireless Mobile Sensors

journal, February 2014

- Mahboubi, Hamid; Moezzi, Kaveh; Aghdam, Amir G.
- IEEE Transactions on Industrial Informatics, Vol. 10, Issue 1

##
Spatially-distributed coverage optimization and control with limited-range interactions

journal, September 2005

- Cortés, Jorge; Martínez, Sonia; Bullo, Francesco
- ESAIM: Control, Optimisation and Calculus of Variations, Vol. 11, Issue 4

##
Unicycle Coverage Control Via Hybrid Modeling

journal, February 2010

- Kwok, A.; Martinez, S.
- IEEE Transactions on Automatic Control, Vol. 55, Issue 2

##
Centroidal Area-Constrained Partitioning for Robotic Networks

journal, March 2014

- Patel, Rushabh; Frasca, Paolo; Bullo, Francesco
- Journal of Dynamic Systems, Measurement, and Control, Vol. 136, Issue 3

##
Differentiation Under the Integral Sign

journal, June 1973

- Flanders, Harley
- The American Mathematical Monthly, Vol. 80, Issue 6

##
Differentiation Under the Integral Sign

journal, June 1973

- Flanders, Harley
- The American Mathematical Monthly, Vol. 80, Issue 6

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*