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Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking. 

Zero-shot learning (ZSL) for image classification focuses on recognizing novel categories that have no labeled data available for training. The learning is generally carried out with the help of mid-level semantic descriptors associated with each class. This semantic-descriptor space is generally shared by both seen and unseen categories. However, ZSL suffers from hubness, domain discrepancy and biased-ness towards seen classes. To tackle these problems, we propose a three-step approach to zero-shot learning. Firstly, a mapping is learned from the semantic-descriptor space to the image- feature space. This mapping learns to minimize both one-to- one and pairwise distances between semantic embeddings and the image features of the corresponding classes. Secondly, we propose test-time domain adaptation to adapt the semantic embedding of the unseen classes to the test data. This is achieved by finding correspondences between the semantic descriptors and the image features. Thirdly, we propose scaled calibration on the classification scores of the seen classes. This is necessary because the ZSL model is biased towards seen classes as the unseen classes are not used in the training. Finally, to validate the proposed three-step approach, we performed experiments on four benchmark datasets where the proposed method outperformed previous results. We also studied and analyzed the performance of each component of our proposed ZSL framework.