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Grab bars have been widely used for assisting elderly people with mobility and providing support for daily activities. This work aims to expand the notion of grab bars beyond fixed installations by the use of a mobile robot that can place a handlebar at any point in space, to optimally support postural transitions. A survey of elderly people and care professionals indicated that such a device must be sturdy, providing secure support without sliding or tipping over, yet also have a compact footprint to be maneuverable within confined spaces. Here, we propose a novel two-body robot structure, consisting of two small-footprint mobile bases connected by a four bar linkage where handlebars are mounted. Each base measures only 29.2 cm wide, making the robot likely the slimmest ever developed for mobile postural assistance. Through kinematic analysis, it is shown that the two-body structure can bear the entire weight of a human body, meeting required load bearing specifications as a handlebar. A control plan is proposed that is generalizable to all robots with two nonholonomic mobile bases connected by a coupling mechanism. This consists of a leader-follower scheme, in which the bases are connected by a virtual spring, as well as various enhancements to waypoint tracking and dead reckoning that allow the robot to smoothly and accurately follow a series of waypoints. A prototype robot is constructed, and its performance is validated experimentally. 

This paper presents a computational method, called Bootstrapped Koopman Direct Encoding (B-KDE) that allows us to approximate the Koopman operator with high accuracy by combining Koopman Direct Encoding (KDE) with a deep neural network. Deep learning has been applied to the Koopman operator method for finding an effective set of observable functions. Training the network, however, inevitably faces difficulties such as local minima, unless enormous computational efforts are made. Incorporating KDE can solve or alleviate this problem, producing an order of magnitude more accurate prediction. KDE converts the state transition function of a nonlinear system to a linear model in the lifted space of observables that are generated by deep learning. The combined KDE-deep model achieves higher accuracy than that of the deep learning alone. In B-KDE, the combined model is further trained until it reaches a plateau, and this computation is alternated between the neural network learning and the KDE computation. The result of the MSE loss implies that the neural network may get rid of local minima or at least find a smaller local minimum, and further improve the prediction accuracy. The KDE computation however, entails an effective algorithm for computing the inner products of observables and the nonlinear functions of the governing dynamics. Here, a computational method based on the Quasi-Monte Carlo integration is presented. The method is applied to a three-cable suspension robot, which exhibits complex switched nonlinear dynamics due to slack in each cable. The prediction accuracy is compared against its traditional counterparts. 

Falls may cause serious injuries to older adults, leading to a deteriorated quality of life. Currently, there is a lack of fall injury prevention devices, especially for the balance impaired population who rely on mobility aids. Here, the functionality of a walker is augmented, so that it can predict a fall in real-time and prevent fall injuries via a rapidly reconfigurable mechanism. A key challenge is real-time fall prediction, which is a time-critical decision making process. A fall must be predicted preemptively so that the system has sufficient time to deploy the injury prevention mechanism. Data are collected from human subjects undergoing diverse loss-of-balance situations while using a walker. A predictor based on multiple Long-Short Term Memory (LSTM) networks is constructed based on three novel techniques. First, diverse fall types are identified by separately learning fast and slow falls. Second, a "Timer LSTM" is constructed that estimates the time remaining before an imbalance is unrecoverable and the fall prevention mechanism must be activated. Then if time allows, additional data are collected and the possibility of a fall is further examined. This approach lowered the fall prediction false positive rate. Third, confounding cases are further analyzed using a metric of data deficiency, called the Lipschitz quotient. Additional data features that lower the Lipschitz quotients and, thereby, increase data predictability, are sought and incorporated into the original input signals. Augmenting the data further improved performance, and the best model had a 97% success rate at identifying falls at a 0.17% false positive rate. The prediction method is implemented on a novel walkertype fall prediction and prevention prototype. The walker has a small footprint for improved maneuverability, and becomes untippable when its expandable legs are deployed in the event of a predicted fall. Thus, the older adult tethered to the untippable walker is protected from a fall. This work introduces techniques to improve the performance of real-time fall predictors when limited data is available, identifies how to select fruitful features from the available sensor signals, and incorporates a fall predictor into a physical device for a rapid fall injury prevention response. This promises immense benefits for future research on improving older adult wellbeing through real-time fall protection. 

The dynamic complexity of robots and mechatronic systems often pertains to the hybrid nature of dynamics, where governing equations consist of heterogenous equations that are switched depending on the state of the system. Legged robots and manipulator robots experience contact-noncontact discrete transitions, causing switching of governing equations. Analysis of these systems have been a challenge due to the lack of a global, unified model that is amenable to analysis of the global behaviors. Composition operator theory has the potential to provide a global, unified representation by converting them to linear dynamical systems in a lifted space. The current work presents a method for encoding nonlinear heterogenous dynamics into a high dimensional space of observables in the form of Koopman operator. First, a new formula is established for representing the Koopman operator in a Hilbert space by using inner products of observable functions and their composition with the governing state transition function. This formula, called Direct Encoding, allows for converting a class of heterogenous systems directly to a global, unified linear model. Unlike prevalent data-driven methods, where results can vary depending on numerical data, the proposed method is globally valid, not requiring numerical simulation of the original dynamics. A simple example validates the theoretical results, and the method is applied to a multi-cable suspension system.