SCIENCE CHINA Information Sciences, Volume 63 , Issue 7 : 170201(2020) https://doi.org/10.1007/s11432-019-2748-x

Bio-inspired robotic impedance adaptation for human-robot collaborative tasks

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  • ReceivedJun 18, 2019
  • AcceptedNov 29, 2019
  • PublishedMay 26, 2020


To improve the robotic flexibility and dexterity in a human-robot collaboration task, it is important to adapt the robot impedance in a real-time manner to its partner's behavior. However, it is often quite challenging to achieve this goal and has not been well addressed yet. In this paper, we propose a bio-inspired approach as a possible solution, which enables the online adaptation of robotic impedance in the unknown and dynamic environment. Specifically, the bio-inspired mechanism is derived from the human motor learning, and it can automatically adapt the robotic impedance and feedforward torque along the motion trajectory. It can enable the learning of compliant robotic behaviors to meet the dynamic requirements of the interactions. In order to validate the proposed approach, an experiment containing an anti-disturbance test and a human-robot collaborative sawing task has been conducted.


This work was supported by National Natural Science Foundation of China (Grant Nos. 61861136009, 61811530281).


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  • Figure 2

    (Color online) The diagram of the biomimetic controller.

  • Figure 3

    (Color online) The set-up (a) and the results of the disturbance test of (b) joint S0, (c) joint S1, (d) joint E0, (e) joint E1, (f) joint W0, (g) joint W1, and (h) joint W2.

  • Figure 4

    (Color online) The experimental set-up for the sawing task. (a) The human partner actively pulls the saw. The impedance of the robotic arm increases gradually from a small value to some extent. (b) The robot actively pulls the saw back owing to the large impedance. The human partner relaxes his muscle strength in this phase.

  • Figure 5

    (Color online) The experimental results of the sawing task. (a) Joint S1; (b) joint E1; (c) joint W0; (d) joints S0, E0, W0, and W2.


    Algorithm 1 The online learning of the robotic compliant movement

    Require:The desired robot arm posture $(q_{0},~~\dot{q}_{0})$;

    Output: The computed joint torque command $~\tau_{c}^{t}~$ by (2) at each time step;

    Initialize the stiffness and damping matrix as $~K^{0}=\text{diag}\lbrace0,0,~\ldots,~0\rbrace~$ and $~D^{0}=\text{diag}\lbrace0,0,~\ldots,~0\rbrace~$;

    Initialize the feedforward vector as $~u^{0}=\text{diag}\lbrace0,0,~\ldots,~0\rbrace~$;

    Set the constant coefficients $\pi~$, $~\delta$, $a$, and $~b~$;

    Set the constant parametric vectors $~\alpha~$ and $~\beta~$;

    Set the stiffness range $~K^{\text{max}}~$ and $~K^{\text{min}}~$;

    for each time step $t~\in~[1,T]$

    Get the current robot joint states $~q~$ and $~\dot{q}~$;

    Compute the angle error and the velocity error according to (4);

    Compute the sliding error according to (8);

    Compute the vector $~\gamma~$ according to (16);

    Update the feedforward torque $~u^{t+1}=u^{t}~+~\Delta~u~$, using (15);

    Update the stiffness matrix $~K^{t+1}=K^{t}~+~\Delta~K~$, using (17);

    Adjust the stiffness values in a proper range based on (18);

    Compute the damping matrix $~D^{t+1}~$;

    Compute the impedance term $~v^{t+1}~$;

    Compute the joint torque $~\tau_{c}^{t+1}~$, using (2);

    Send the joint torque command to the robotic joint motors;

    end for

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