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Force/motion control of constrained mobile manipulators including actuator dynamics

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Abstract

This paper deals with the force and motion control problem of holonomic constrained nonholonomic mobile manipulators by including actuator dynamics with the manipulator’s dynamics. Even though, the force/motion control problem of holonomic constrained nonholonomic mobile manipulators has been enthusiastically studied. But there is little research on the force/motion control of rigid-link electrically driven mobile manipulators. Considering the actuator dynamics together with the manipulator’s dynamics, the controller is designed not only at the dynamic level, but also at the actuator level. This class of rigid link electrically driven electromechanical systems can be disturbed with the structured and unstructured uncertainties and disturbances. The structured and unstructured uncertainties and the coupling terms between the mobile base and the robotic arm can not be handled properly by the model-based controller. Also it is not possible to get the exact knowledge of dynamical model in real applications. Therefore, a model-based control scheme is combined with the RBF neural network based model-free control scheme for the approximation of the nonlinear mechanical dynamics. In order to compensate for the deviations due to the presence of the external disturbances, friction terms, and reconstruction error of the neural network, an adaptive bound part is also added to the controller. Moreover for the approximation of the unknown electrical dynamics, RBF neural network is employed. The designed control scheme provides that the position tracking errors and the constraint force congregate to the desired levels asymptotically. The designed control scheme also controls the direct current motors, being used to provide the desired currents and torques. The Lyapunov theorem is utilized to prove the stability of the designed controller. Finally, to illustrate the designed control scheme, numerical simulation results are produced in a comparative manner to show superior robustness in coping with the uncertainties.

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Abbreviations

\(\hbox {RLED}\) :

Rigid link electrically driven

\(\hbox {RBF}\) :

Radial basis function

t :

Time

\(q_{b}\in R^{h_{b}}\) :

Mobile base coordinate vector

\(q_{\upsilon }\in R^{h_{\upsilon }}\) :

Mobile arm coordinate vector

\(\lambda ={[}\lambda _{{\upsilon }},\lambda _{{b}}{]}^{{T}}\) :

Lagrangian multiplier allied to holonomic and nonholonomic constraints

\(\tau \in R^{p}\) :

Torque input vector

\(p_1\) :

Holonomic constraints

\(k_1\) :

Nonholonomic constraints

U :

Voltage control input vector

I :

Armature current vector

\({\dot{\theta }}_l, {\dot{\theta }}_r\) :

Left and right angular velocities of the wheel

\(\upsilon \) :

Mobile base linear velocity

\(K_{\beta }, K_l\) :

Positive definite matrices

\(B_{1\upsilon }, B_{1b}\) :

Input matrix for the mobile arm and the mobile base

\(d_1,d_2, d_3\) :

Finite constants

\(r_1\) :

Filtered tracking error

\(e_I\) :

Current error

\(y, y_1\) :

Number of nodes

\( x, x_1\) :

Input vectors

\( t_1, t_2\) :

Number of output vectors

\( \varGamma _W, \varGamma _{W_{1}}, \varGamma _\phi \) :

Positive definite matrices

\(\epsilon (x), {\epsilon _1}(x_1)\) :

Positive constants

\( \varUpsilon \) :

Adaptive bound part

\( \gamma , \delta \) :

Positive constants

\(e_{\beta }, {\dot{e}}_{\beta }\) :

Position and velocity error

\(\phi \in R^{k}\) :

Parameter vectors

\(L^2\) :

Performance index

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Acknowledgements

The presented work was supported by the University Grants Commission(UGC) Sr. No. 2121240927 with Ref No. 23/12/2012 (ii) EU-V, New Delhi, India.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Kurukshetra, Haryana, 136119, India

    Manju Rani & Naveen Kumar

  2. Cluster Innovation Centre, University of Delhi, New Delhi, India

    Harendra Pal Singh

Authors
  1. Manju Rani
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  2. Naveen Kumar
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  3. Harendra Pal Singh
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Correspondence to Naveen Kumar.

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Rani, M., Kumar, N. & Singh, H.P. Force/motion control of constrained mobile manipulators including actuator dynamics. Int. J. Dynam. Control 7, 940–954 (2019). https://doi.org/10.1007/s40435-019-00523-y

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  • DOI: https://doi.org/10.1007/s40435-019-00523-y

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