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This work proposes a modular learning framework (MIRA) for rehabilitation robots based on a new deep recurrent neural network (RNN) that achieves adaptive multi-joint motion imitation. The RNN is fed with the fundamental frequencies as well as the ranges of the joint trajectories, in order to predict the future joint trajectories of the robot. The proposed framework also uses a Segment Online Dynamic Time Warping (SODTW) algorithm to quantify the closeness between the robot and patient motion. The SODTW cost decides the amount of modification needed in the inputs to our deep RNN network, which in turn adapts the robot movements. By keeping the prediction mechanism (RNN) and adaptation mechanism (SODTW) separate, the framework achieves modularity, flexibility, and scalability. We tried both Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) RNN architectures within our proposed framework. Experiments involved a group of 15 human subjects performing a range of motion tasks in conjunction with our social robot, Zeno. Comparative analysis of the results demonstrated the superior performance of the LSTM RNN across multiple task variations, highlighting its enhanced capability for adaptive motion imitation. 

In an optimal design problem, we are given a set of linear experiments v1,…,vn∈Rd and k≥d, and our goal is to select a set or a multiset S⊆[n] of size k such that Φ((∑i∈Sviv⊤i)−1) is minimized. When Φ(M)=Determinant(M)1/d, the problem is known as the D-optimal design problem, and when Φ(M)=Trace(M), it is known as the A-optimal design problem. One of the most common heuristics used in practice to solve these problems is the local search heuristic, also known as the Fedorov’s exchange method (Fedorov, 1972). This is due to its simplicity and its empirical performance (Cook and Nachtrheim, 1980; Miller and Nguyen, 1994; Atkinson et al., 2007). However, despite its wide usage no theoretical bound has been proven for this algorithm. In this paper, we bridge this gap and prove approximation guarantees for the local search algorithms for D-optimal design and A-optimal design problems. We show that the local search algorithms are asymptotically optimal when kd is large. In addition to this, we also prove similar approximation guarantees for the greedy algorithms for D-optimal design and A-optimal design problems when kd is large.