Attractor dynamics approach to joint transportation by autonomous robots: theory, implementation and validation on the factory floor

Abstract

This paper shows how non-linear attractor dynamics can be used to control teams of two autonomous mobile robots that coordinate their motion in order to transport large payloads in unknown environments, which might change over time and may include narrow passages, corners and sharp U-turns. Each robot generates its collision-free motion online as the sensed information changes. The control architecture for each robot is formalized as a non-linear dynamical system, where by design attractor states, i.e. asymptotically stable states, dominate and evolve over time. Implementation details are provided, and it is further shown that odometry or calibration errors are of no significance. Results demonstrate flexible and stable behavior in different circumstances: when the payload is of different sizes; when the layout of the environment changes from one run to another; when the environment is dynamic—e.g. following moving targets and avoiding moving obstacles; and when abrupt disturbances challenge team behavior during the execution of the joint transportation task.

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Notes

  1. 1.

    Note that, although the vector field \(f_r(\phi _r)\) (r = Leader, Helper) changes, as the robot moves or the sensorial information changes, these dynamical systems are autonomous, since \(f_r(\phi _r)\) does not explicitly depend on time.

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Acknowledgements

This work was supported by FCT—Fundação para a Ciência e Tecnologia within the scope of the Project PEst-UID/CEC/00319/2013 and by the Ph.D. Grants SFRH/BD/38885/2007 and SFRH/BPD/71874/2010, as well as funding from FP6-IST2 EU-IP Project JAST (Proj. Nr. 003747). We would like to thank the anonymous reviewers, whose comments have contributed to improve the paper.

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Correspondence to Estela Bicho.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mp4 1015 KB)

Supplementary material 2 (mp4 1205 KB)

Supplementary material 3 (mp4 5410 KB)

10514_2018_9729_MOESM4_ESM.mp4

Supplementary material 4 (mp4 7444 KB)

Supplementary material 5 (mp4 7248 KB)

Supplementary material 4 (mp4 7444 KB)

Appendices

Appendix A: Robot kinematics

The path velocity, v, and angular velocity, \(\omega \), of our robotic platforms were controlled by setting the linear speeds of the two driving wheels as follows:

$$\begin{aligned} v_{right}= & {} v+\frac{D_{wheels}}{2}\omega \end{aligned}$$
(37)
$$\begin{aligned} v_{left}= & {} v-\frac{D_{wheels}}{2}\omega \end{aligned}$$
(38)

where \(D_{wheels}\) is the distance between the two driving wheels. \(\omega = d\phi /dt\) is obtained directly from the behavioral dynamics for the heading direction, Eq. 25, and v results from integrating Eq. 27, by following a Euler method, i.e., \(v = v +dt.g(v)\), with dt being the time step.

Appendix B: Values of parameters used in the experiments

\(N_{L} = 11\); \(N_{H} = 21\); \(\delta _{L} = \pi /8\); \(\delta _{H} = \pi /16\); \(\beta _{1,r} = 2\); \(\beta _{2,r} = 0.5 \times C_{l}\), where \(C_{l}\) is the cargo’s length; \(\varPsi _{vir,L} = \pi /4\); \(\varPsi _{thres} = \pi /6\); \(\lambda _{desvir,L} = 0.4\); \(\lambda _{desvir,H} = 0.5\); \(\mu _{1} = 2\); \(\mu _{2} = 2\); \(\sqrt{\mathcal {Q}_{r}} = 0.01\); \(\varPsi _{v} = \pi /4\); \(\gamma _{max} = 5\pi /12\); \(\lambda _{v,L} = 10/3\); \(\lambda _{v,H} = 2\); \(V_{des,L} = 0.3\); \(\mu _{s} = 1\); \(D_{c,max} = 0.2\); \(\mu _{obs} = 7\); \(D_{obs,min} = 0.1\); \(D_{obs,max} = 1.5\); \(k_{stop} = 2\); \(d_{stop} = 1.25\). \(D_{wheels} = 45\) cm. \(dt \approx 50\) ms.

Appendix C: Videos

In the supplementary material one can find the following videos, which further complement the results:

Video #1 : illustrates the capacity of the robot team to transport the cargo while following moving targets and the ability to cope with environments that change in layout.

Video #2: demonstrates the capacity of the robot team to transport cargos of different sizes in U-turn scenarios.

Video #3: demonstrates the capacity of the robot team to avoid moving obstacles.

Video #4: shows the capability of the robot team to avoid abrupt perturbations that may appear during the joint transportation task.

Video #5: shows the robot team navigating on a factory floor, where their joint transportation behavior is challenged by a cluttered environment, with narrow passages and a moving obstacle (human operator driving a pallet stacker).

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Machado, T., Malheiro, T., Monteiro, S. et al. Attractor dynamics approach to joint transportation by autonomous robots: theory, implementation and validation on the factory floor. Auton Robot 43, 589–610 (2019). https://doi.org/10.1007/s10514-018-9729-2

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Keywords

  • Joint transportation
  • Autonomous robots
  • Mobile robots
  • Obstacle avoidance
  • Unknown environments
  • Attractor dynamics