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Adaptive obstacle avoidance in path planning of collaborative robots for dynamic manufacturing

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Abstract

Gaussian Mixture Model (GMM)/Gaussian Mixture Regression (GMR) is a paramount technology of learning from demonstrations to perform human–robotic collaboration. However, GMM/GMR is ineffective in supporting dynamic manufacturing where random obstacles in the applications generate potential safety concerns. In this paper, an improved GMM/GMR-based approach for collaborative robots (cobots) path planning is designed to achieve adaptive obstacle avoidance in dynamic manufacturing. The approach is realised via three innovative steps: (i) new quality assessment criteria for a cobot’s paths produced by GMM/GMR are defined; (ii) based on the criteria, demonstrations and parameters of GMM/GMR are adaptively amended to eliminate collisions and safety issues between a cobot and obstacles; (iii) a fruit fly optimisation algorithm is incorporated into GMM/GMR to expedite the computational efficiency. Case studies with different complexities are used for approach validation in terms of feature retention from demonstrations, regression path smoothness and obstacle avoidance effectiveness. Results of the case studies and benchmarking analyses show that the approach is robust and efficient for dynamic manufacturing applications.

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Abbreviations

GMM:

Gaussian mixture modelling

GMR:

Gaussian mixture regression

FFO:

Fruit fly optimisation

EM:

Expectation-maximisation

LfD:

Learning from demonstrations

K :

The total number of Gaussian clusters

\({\varvec{\mu}}_{{\varvec{i}}}\) :

The mean of the i-th Gaussian cluster

\({\varvec{\sigma}}_{{\varvec{i}}}\) :

The covariance of the i-th Gaussian cluster

\(N_{i} ({\varvec{p}}_{j} |{\varvec{\mu}}_{{\varvec{i}}} ,{\varvec{\sigma}}_{{\varvec{i}}} )\) :

The probability density function of the i-th Gaussian cluster

\(LL\) :

Log of the likelihood function of demonstrations

\({\varvec{p}}_{j}\) :

A constructive point from demonstrations

\({\varvec{a}}_{i1}\) :

Eigenvector/direction of the major axis of the i-th Gaussian cluster

\({\varvec{a}}_{i2}\) :

Eigenvector/direction of the minor axis of the i-th Gaussian cluster

\(\sqrt {\lambda_{i1} }\) :

Length of the major axis of the i-th Gaussian cluster

\(\sqrt {\lambda_{i2} }\) :

Length of the minor axis of the i-th Gaussian cluster

D :

The dimension of the demonstration data

\(t\) :

Time-step

\(x_{j} ,y_{j} ,z_{j}\) :

The coordinate of the j-th point in original demonstrations

\(x_{j}^{{\prime }} ,y_{j}^{{\prime }} ,z_{j}^{{\prime }}\) :

The coordinate of the j-th point in Gaussian noise-enhanced points of demonstrations

\(\mu_{x{\text{-}}noise} ,\mu_{y{\text{-}}noise} ,\mu_{z{\text{-}}noise}\) :

Mean of Gaussian noises of x-dimension, y-dimension, z-dimension

\(\sigma_{x{\text{-}}noise} ,\sigma_{y{\text{-}}noise} ,\sigma_{z{\text{-}}noise}\) :

Variance of Gaussian noises of x-dimension, y-dimension, z-dimension

\(r_{x} ,r_{y} ,r_{z}\) :

Random value, which are considered as the noises of x- dimension, y-dimension, z-dimension

\(K\left( i \right)\) :

The curvature of the i-th point of a path

\(\widetilde{{K_{path} }}\) :

The overall average curvature of a path

N :

The number of demonstrations

\({\varvec{var}}_{d\left( y \right)} \left[ t \right]\) :

The variance of the t-th point of the demonstrations in the y-dimension

\({\varvec{var}}_{d\left( x \right)} ,{\varvec{var}}_{d\left( x \right)} ,{\varvec{var}}_{d\left( z \right)}\) :

Variance of all the points in the demonstrations in the x-dimension, y-dimension and z-dimension

\({\varvec{var}}_{d\_r\left( y \right)} \left[ t \right]\) :

Variance of the t-th point of the demonstrations and the regression path in the y-dimension

\({\varvec{var}}_{d\_r\left( x \right)} ,{\varvec{var}}_{d\_r\left( y \right)} ,{\varvec{var}}_{d\_r\left( z \right)}\) :

Variance of all the points of the demonstrations and the regression path in the x-dimension, y-dimension and z-dimension

\( x_{j}^{{\prime \prime }} , y_{j}^{{\prime \prime }} ,z_{j}^{{\prime \prime }}\) :

The new coordinates of the t-th point of the demonstration with noises after the translation process

U :

A unit vector of the points moving direction

d safety :

The pre-set safety distance

RN :

A random value following a standard Gaussian distribution

R w :

The width of the enveloping area of the obstacle

dis :

The minimum distance between new regression path and the dangerous points of the obstacle

SF :

Pre-set safety threshold

\(S_{i} ,\Delta_{i}\) :

The flying distance of an individual fruit fly

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Acknowledgements

This research was sponsored by the National Natural Science Foundation of China (Project No. 51975444), and partially funded by the UK industrial and research partners (the Unipart Powertrain Application Ltd. (UK) and the Institute of Digital Engineering (UK)).

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Authors and Affiliations

  1. School of Logistics Engineering, Wuhan University of Technology, Wuhan, China

    Yudie Hu, Yuqi Wang, Kaixiong Hu & Weidong Li

  2. Faculty of Engineering, Environment and Computing, Coventry University, Coventry, UK

    Weidong Li

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  1. Yudie Hu
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  2. Yuqi Wang
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Correspondence to Weidong Li.

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Hu, Y., Wang, Y., Hu, K. et al. Adaptive obstacle avoidance in path planning of collaborative robots for dynamic manufacturing. J Intell Manuf 34, 789–807 (2023). https://doi.org/10.1007/s10845-021-01825-9

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