Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2399–2411 | Cite as

A New Hybrid Position/Force Control Scheme for Coordinated Multiple Mobile Manipulators

  • Manju Rani
  • Naveen KumarEmail author
Research Article - Electrical Engineering


In this paper, a new hybrid position/force control scheme is proposed for coordinated multiple mobile manipulators holding a rigid object. The problem of the controller design for multiple mobile manipulators is much complicated as compared to single mobile manipulator. Many of the position/force control schemes for coordinated multiple mobile manipulators assume exact knowledge of the dynamical model. But the dynamic model of the coordinated multiple mobile manipulators is highly uncertain and faces external disturbances, uncertain environment intervention, etc. Therefore, model-based controller is inadequate to deal with such uncertain systems. In the proposed scheme, the inefficiency of the model-based controller is recovered by combining with RBF neural network-based mode-free controller along with a compensation controller. RBF neural network is utilized to estimate the unmodeled dynamics of the system without requiring the offline learning. The compensation controller is utilized to neutralize the effects of the friction terms, external disturbances, and the network reconstruction error. The online adaptation of the weights and the parameter updates are utilized in the Lyapunov function to make the system to be stable. Furthermore, the proposed control scheme assures that both the position and the internal force trajectory errors converge asymptotically. To depict the adequacy of the proposed control scheme, simulation results are provided with different existing controllers in a comparative manner.


Coordinated mobile manipulators Hybrid position/force control Model-based control RBF neural network Asymptotical stable 

List of symbols


Number of mobile manipulators

\(q_{bi}\in R^{p_{bi}}\)

Generalized coordinate vector for mobile base

\(q_{mi}\in R^{p_{mi}}\)

Generalized coordinate vector for mobile arm

\(\lambda _{i}\in R^{p}\)

Lagrangian multiplier associated with the mobile base and the manipulator’s arm

\(\tau _i \in R^{t}\)

Torque input vector for ith manipulator

\(\mu _{i}\)

Joint position vector for the ith manipulator

\(f_i\in R^{p}\)

Interacting force between the end-effector of the ith manipulator and the object

\({\varTheta _i}(q_{bi})\in R^{p_{bi}\times (p_{bi}-k)}\)

A smooth and linearly independent set of vector fields


Coordinate vector of the object frame


Dimension of the operational coordinate of the object

\(F_{1}\in R^{p_o}\)

Resultant force vector acting at the center of mass of the object

\(F_{I}\in R^{h(p-k)}\)

Internal force vector

\(J_o(y_o)\in R^{h(p-k)\times {p_o}}\)

Jacobian matrix from the object’s frame to the manipulator’s end-effector frame

\(y_{ei}\in R^{p-k}\)

Position and the orientation vector of the ith manipulator

\(s_i>0\)\((1\leqslant {i}\leqslant 3)\)

Finite constants

\(K_{o}\), \(K_{f}\), \(K_{d}\)

Positive definite gain matrices

\(y \in R^{5l}\)

Input vector


Number of nodes of the neural network

\(\varepsilon _N\)

An arbitrary small positive constant

\(\varepsilon (y)\)

Neural network reconstruction error

\(\varPsi (y)\)

Gaussian activation function

\(\gamma , \delta \)

Positive constants

\(\varphi \in R^{s}\)

Parameter vector

\(\varGamma _\varPi \)\(\varGamma _\varphi \)

Positive definite symmetric matrices

\(L ^2\)

Performance index


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We are grateful to University Grants Commission (UGC) Sr. No. 2121240927 with Ref No. 23/12/2012 (ii) EU-V, New Delhi, India for their financially support.


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyKurukshetraIndia

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