Towards Partner-Aware Humanoid Robot Control Under Physical Interactions

Abstract

The topic of physical human-robot interaction received a lot of attention from the robotics community because of many promising application domains. However, studying physical interaction between a robot and an external agent, like a human or another robot, without considering the dynamics of both the systems may lead to many shortcomings in fully exploiting the interaction. In this paper, we present a coupled-dynamics formalism followed by a sound approach in exploiting helpful interaction with a humanoid robot. In particular, we propose the first attempt to define and exploit the human help for the robot to accomplish a specific task. As a result, we present a task-based partner-aware robot control techniques. The theoretical results are validated by conducting experiments with two iCub humanoid robots involved in physical interaction.

A Appendix: Sketch of Proof of Lemma 1

Proof: The stability of $\widetilde{\chi }$ can be analyzed by considering the following Lyapunov function:

(25)

where $K_d, K_p \in \mathbb {R}^{p \times p}$ are two symmetric, positive-definite matrices. Now, on differentiating (25) and using the robot dynamics (1b) along with the force decomposition (18) obtained through coupled-dynamics, we get:

$$\begin{aligned} \dot{\mathrm {V}} = - \ \widetilde{\chi }^T \ K_D \ \widetilde{\chi } \ + \widetilde{\chi }^T \ [ \ \alpha - \ max(0,\alpha )\ ] \ \widetilde{\chi }^{\parallel } \end{aligned}$$

(26)

where,

$$\begin{aligned} \dot{\mathrm {V}} = - \ \widetilde{\chi }^T \ K_D \ \widetilde{\chi } \quad \quad \forall \ \alpha > 0 \end{aligned}$$

$$\begin{aligned} \dot{\mathrm {V}} = - \ \widetilde{\chi }^T \ K_D \ \widetilde{\chi } \ + \widetilde{\chi }^T \ \alpha \ \widetilde{\chi }^{\parallel } \quad \quad \forall \ \alpha \le 0 \end{aligned}$$

The fact that the human joint torques help the robot to perform a control action is encompassed in the right-hand side of the above equation. The component of human joint torques projected in the direction parallel to the task i.e. $\alpha$ makes the Lyapunov function decrease faster. Thus the control law (23) ensures that $\dot{\mathrm {V}} \le 0$ which proves that the trajectories are globally bounded. From Lyapunov theory, as $\dot{\mathrm {V}} \le 0$ in the neighborhood of the point (0, 0) the equilibrium point (22) is stable. The complete proof of Lemma 1 is beyond the scope of this paper due to the space limitations and it will be presented in full in our forthcoming journal publication.