Generation of comfortable lifting motion for a human transfer assistant robot

Abstract

Moving a patient between a bed and a wheel-chair is one of the most burdensome nursing-care tasks for caregivers. Various kinds of transfer assistant robots have been proposed previously. However, designing comfortable transfer motions for individuals has not been intensively studied due to the difficulty of modeling such physical human-robot interactions in conjunction with user preference. To lift a patient from a bed, a robot should raise the patient’s body from the supine posture to a holding posture. In this research, we proposed two different methods for generating lifting motions comfortable for users: (1) a model-based method for estimating the holding posture, and (2) a model-free method based on Bayesian optimization for generating the raising motion. A comfortable holding posture can be generated using human-robot interactive models by reducing the load and pain sensation in simulation, without user trials. To reduce the load, a musculoskeletal model is developed to estimate muscle force considering human-robot physical interactions. To reduce pain, a softness distribution model of the human body is also created to control the robot to contact the human body at a softer place. The motion for raising the human body from the supine posture to the estimated holding posture can be generated with the model-free method from the user’s feedback (scalar value) in terms of the comfort level. Using Bayesian optimization, the number of required trials with physical interactions between user and robot can be reduced to ease the user’s burden. To verify the effectiveness of the proposed methods, we conducted experiments with a dual arm robotic system and human subjects. We search for the most comfortable holding posture based on the developed human models and compare it with the measured value of subjects in the experiment. To generate the raising motion, the experimental result shows that our method can optimize a user-comfortable care motion controller for each individual efficiently.

Appendix: Bayesian optimization using Gaussian processes

Bayesian optimization permits a utility-based selection of the next observation to make on the objective function, which takes into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation).

The actual process of the Bayesian optimization can be achieved by repeatedly taking the following steps until the convergence:

• Step 1: Train a response surface $\hat{f}(\theta )$ from data $\mathcal {D}$ (initially $\emptyset$)

• Step 2: Find $\theta ^*$ that maximizes the acquisition surface $\alpha (\theta )$ which can be computed with the current model of $\hat{f}(\theta )$

• Step 3: Evaluate $\theta ^*$ for the real system to obtain the result $r^*$

• Step 4: Add $\{\theta ^*, r^*\}$ to $\mathcal {D}$ and back to Step 2 until convergence.

More details of Steps 1 and 2 are explained next.

1.1 Learning response surface using Gaussian processes (Step 1)

To create the response surface model that maps $\hat{f}(\cdot ): \pi (\theta ) \mapsto r$, we make use of Bayesian non-parametric GP regression (Rusmassen and Williams 2005). A GP is a distribution over functions $\hat{f} \sim \mathcal {GP}(m_f, k_f)$, fully defined by a prior mean $m_f$ and a co-variance function $k_f$. We assume a model where we observe noisy function values $r=\hat{f}(\theta ) + \epsilon$, where $\epsilon \sim \mathcal {N}(0,\sigma ^2_e)$ is Gaussian noise.

With the above assumptions, having the observations $\mathcal {D}_{1:T} = \{\theta _{1:T}, r_{1:T} \}$, in the previous $t=1:T$ experiments, we can compute the predictive distribution over the functions by Bayes theorem as follows:

$$\begin{aligned} p(f'|\mathcal {D}_{1:T}, \theta ') = \mathcal {N} (\mu (\theta '), \sigma ^2 (\theta ')), \end{aligned}$$

(10)

where

$$\begin{aligned} \mu (\theta ') = \varvec{k}^T \varvec{K}^{-1} \varvec{r} \end{aligned}$$

(11)

$$\begin{aligned} \sigma ^2(\theta ') = k(\theta ', \theta ') - \varvec{k}^t \varvec{K}^{-1} \varvec{k}, \end{aligned}$$

(12)

and $\varvec{k} = [k(\theta _1,\theta ') \ldots , k(\theta _T,\theta '))]$, $\varvec{r} = [r_1,\ldots ,r_T]$, i-jth element of $\varvec{K}$ is $k(\theta _i, \theta _j)$.

1.2 Obtaining and optimizing the acquisition surface $\alpha (\theta )$ (Step 2)

The expectation of the response surface learned by the predictive distribution of the Gaussian process enables us to balance the trade-off of exploiting and exploration. When exploring, we should choose points where the surrogate variance is large. When exploiting, we should choose points where the surrogate mean is high.

A reasonable implementation of such a trade-off is achieved by utilizing the upper confidence bound (UCB) of the prediction.

$$\begin{aligned} \alpha (\theta ) := \mathrm{UCB(\theta )} = \mu (\theta ) + \kappa \sigma (\theta ), \end{aligned}$$

(13)

where $\kappa \ge 0$ is the weight parameter. The theoretical analysis on how to optimally set the parameter is given by Srinivas et al. (2010). Thus, we utilize UCB as the acquisition function.

Once the acquisition surface $\alpha (\theta )$ is computed, the parameter to be tested is found by the following maximization:

$$\begin{aligned} \theta ^* \leftarrow \mathop {\arg \;\max }\limits _{{\theta } \in {\varvec{R}^d}} \alpha (\theta ). \end{aligned}$$

(14)