Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Energy-Aware Task Allocation for Teams of Multi-mode Robots

Takumi Ito, Riku Funada, Mitsuji Sampei, Gennaro Notomista

TL;DR

Problem: energy-aware MRTA for teams of robots with switchable modes; aim to jointly allocate tasks and select execution modes to optimize energy use and resilience. Approach: encode multimodality using a graph-based representation with a virtual-robot layer, define mapping matrices $F$, $T$, $S$, and $\Pi$ to capture capabilities and task requirements, and solve a mixed-integer quadratic program that incorporates Control Barrier Function constraints; extend to high relative degree dynamics using integral CBFs and derive linear matrix inequalities for convergence. Contributions: (1) a unified multi-mode MRTA framework; (2) constraint-based task execution applicable to high relative degree dynamics; (3) convergence guarantees via LMIs; (4) simulations demonstrating energy-aware mode switching and resilience under regulatory restrictions. Significance: enables energy-efficient, resilient coordination of heterogeneous robots across diverse tasks and environments.

Abstract

This work proposes a novel multi-robot task allocation framework for robots that can switch between multiple modes, e.g., flying, driving, or walking. We first provide a method to encode the multi-mode property of robots as a graph, where the mode of each robot is represented by a node. Next, we formulate a constrained optimization problem to decide both the task to be allocated to each robot as well as the mode in which the latter should execute the task. The robot modes are optimized based on the state of the robot and the environment, as well as the energy required to execute the allocated task. Moreover, the proposed framework is able to encompass kinematic and dynamic models of robots alike. Furthermore, we provide sufficient conditions for the convergence of task execution and allocation for both robot models.

Energy-Aware Task Allocation for Teams of Multi-mode Robots

TL;DR

Problem: energy-aware MRTA for teams of robots with switchable modes; aim to jointly allocate tasks and select execution modes to optimize energy use and resilience. Approach: encode multimodality using a graph-based representation with a virtual-robot layer, define mapping matrices , , , and to capture capabilities and task requirements, and solve a mixed-integer quadratic program that incorporates Control Barrier Function constraints; extend to high relative degree dynamics using integral CBFs and derive linear matrix inequalities for convergence. Contributions: (1) a unified multi-mode MRTA framework; (2) constraint-based task execution applicable to high relative degree dynamics; (3) convergence guarantees via LMIs; (4) simulations demonstrating energy-aware mode switching and resilience under regulatory restrictions. Significance: enables energy-efficient, resilient coordination of heterogeneous robots across diverse tasks and environments.

Abstract

This work proposes a novel multi-robot task allocation framework for robots that can switch between multiple modes, e.g., flying, driving, or walking. We first provide a method to encode the multi-mode property of robots as a graph, where the mode of each robot is represented by a node. Next, we formulate a constrained optimization problem to decide both the task to be allocated to each robot as well as the mode in which the latter should execute the task. The robot modes are optimized based on the state of the robot and the environment, as well as the energy required to execute the allocated task. Moreover, the proposed framework is able to encompass kinematic and dynamic models of robots alike. Furthermore, we provide sufficient conditions for the convergence of task execution and allocation for both robot models.

Paper Structure

This paper contains 20 sections, 3 theorems, 24 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. MULTI-MODE ROBOT MODELING
  3. Task-to-mode Mapping
  4. Mapping Matrices
  5. Specialization and Penalty
  6. System Models
  7. Motion Model
  8. Energy Model
  9. TASK EXECUTION AND ALLOCATION
  10. Preliminary: Constraint-Based Task Execution
  11. Task Allocation for Multi-mode Robots
  12. Analysis of Convergence
  13. HIGH RELATIVE DEGREE TASK EXECUTION AND ALLOCATION
  14. Modeling a Convertible UAV
  15. Dynamics
  16. ...and 5 more sections

Key Result

Theorem 1

If $h(x)$ is a CBF, then any Lipschitz continuous controller $u\in\{u ~|~ L_f h(x)+ L_g h(x) u + \gamma(h(x))\geq0\}$ for eq:dynamics renders the zero super-level set $C$ forward invariance and asymptotically stable in $\mathbb{R}^{n_x}$.

Figures (3)

  • Figure 1: Example of mapping, including two tasks, two capabilities, three features, and two robots with two modes. One robot is a UAV with wheels, which has ground vehicle and ground modes, and the other is a convertible UAV, which has hovering and cruise modes.
  • Figure 2: Single UAV simulation. (a) Encoding: Both modes can execute the task. (b) Initial state. (c) Result trajectory: The trajectories of the cruise and hovering mode are shown as solid and dashed lines, respectively.
  • Figure 3: Multiple UAV simulation with a regulation restriction. Each robot is drawn in the same color in all figures. (a) Encoding: Robot 1 has only cruise mode, while the others have both modes. (b) Snapshot of the result at the time $t=0$ s. The result trajectories of the cruise and hovering modes are drawn in solid and dashed lines in the same color of its robot. The cruise mode is prohibited in the brown area. (c) $t=1$ s. (d) $t=2$ s. (e) $t=3$ s. (f) $t=10$ s.

Theorems & Definitions (8)

  • Example 1
  • Definition 1: Control Barrier Function (CBF) robot_ecology
  • Theorem 1: Forward invariance robot_ecology
  • Remark 1
  • Proposition 1
  • proof
  • Proposition 2
  • proof