## 1 Introduction
Different from the above studies, the power-assisted cart in this paper is designed for such a scene: it can carry the belongings of the user, sustain the weight of the user, and provide enough driving force with only minimal effort needed from the user to operate it. This will make it more convenient for the elderly to go outdoors and to participate in social activities, and thus is good for health [23; 24] and the avoidance of cognitive impairment such as dementia [25; 26]. The main objective is to ensure that the cart motor delivers proper walking assistance force under various environmental conditions, including gravity and frictional resistance variation, with high efficiency. Inspired by the fuel efficiency of cars, we propose a performance index for the assessment of operational efficiency while walking with the power-assisted cart (payload). We designed two control methods, namely the optimal assistance ratio (OAR) and the disturbance-observer-based (DOB) methods, for a power-assisted cart named RT.1 developed by Funai Electric Co., Ltd., and RT.WORKS Co., Ltd. Both assist the user by reducing the influence of the environment. The performances of these two methods were evaluated via experimentation by comparing cases without assistance and with default assistance. Eight participants walked with the power-assisted cart at a fixed pace. The performance index for each method to evaluate the operational efficiency and walking speed during assisted walking was calculated from the obtained experimental data. Finally, the drawbacks and applicable scope of the proposed methods are discussed herein. The OAR method is based on a simple idea. Since frictional resistance varies with the road conditions, it is assumed that there is an OAR for each type of road from the data obtained in preliminary studies. Next, a classifier is chosen to recognize the road surfaces with high accuracy. After that, high efficiency needs to hold while walking with the cart on one of these surfaces. The usefulness of the DOB method for walking assistance has been shown in a number of studies [27; 28; 29; 30]. The key idea is that a disturbance observer can estimate and eliminate any existing \"disturbance\". This method has some distinctive merits compared to the OAR one. First, there is no need to estimate the road type; second, it can deal with frictional resistance and gravitational effect together; and third, it still works when no one is operating the cart. The novelty of this study is divided into three parts. First, when the traditional assistance method is implemented in the power-assisted cart, we found that an OAR can be determined for each surface during stable walking via experimental verification. Second, we reveal the efficiency of the two proposed methods and also discuss their disadvantages. According to the experimental results, the scope of the application of each method is also discussed. Third, combining the two methods can overcome the mentioned drawbacks and maintain good performance while walking over a long distance. The results of this study could motivate manufacturers to improve similar existing devices on the market and also provide guidance on how to utilize the proposed methods for practical use.