{
  "id": "1703.01662",
  "version": "v1",
  "published": "2017-03-05T20:51:55.000Z",
  "updated": "2017-03-05T20:51:55.000Z",
  "title": "A dynamical system for prioritizing and coordinating motivations",
  "authors": [
    "Paul B. Reverdy",
    "Daniel E. Koditschek"
  ],
  "comment": "34 pages, submitted",
  "categories": [
    "math.DS",
    "math.OC"
  ],
  "abstract": "We develop a dynamical systems approach to prioritizing multiple tasks in the context of a mobile robot. We take navigation as our prototypical task, and use vector field planners derived from navigation functions to encode control policies that achieve each individual task. We associate a scalar quantity with each task, representing its current importance to the robot; this value evolves in time as the robot achieves tasks. In our framework, the robot uses as its control input a convex combination of the individual task vector fields. The weights of the convex combination evolve dynamically according to a decision model adapted from the bio-inspired literature on swarm decision making, using the task values as an input. We study a simple case with two navigation tasks and derive conditions under which a stable limit cycle can be proven to emerge. While flowing along the limit cycle, the robot periodically navigates to each of the two goal locations; moreover, numerical study suggests that the basin of attraction is quite large so that significant perturbations are recovered with a reliable return to the desired task coordination pattern.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-05T20:51:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G25",
      "37D10",
      "37N35"
    ],
    "keywords": [
      "dynamical system",
      "coordinating motivations",
      "limit cycle",
      "individual task vector fields",
      "robot achieves tasks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}