A neural network-based framework is developed and experimentally demonstrated for the problem of estimating the shape of a soft continuum arm (SCA) from noisy measurements of the pose at a finite number of locations along the length of the arm. The neural network takes as input these measurements and produces as output a finitedimensional approximation of the strain, which is further used to reconstruct the infinite-dimensional smooth posture. This problem is important for various soft robotic applications. It is challenging due to the flexible aspects that lead to the infinitedimensional reconstruction problem for the continuous posture and strains. Because of this, past solutions to this problem are computationally intensive. The proposed fast smooth reconstruction method is shown to be five orders of magnitude faster while having comparable accuracy. The framework is evaluated on two testbeds: a simulated octopus muscular arm and a physical BR2 pneumatic soft manipulator.

In visual Reinforcement Learning (RL), learning from pixel-based observations poses significant challenges on sample efficiency, primarily due to the complexity of extracting informative state representations from high-dimensional data. Previous methods such as contrastive-based approaches have made strides in improving sample efficiency but fall short in modeling the nuanced evolution of states. To address this, we introduce MOOSS, a novelframe-work that leverages a temporal contrastive objective with the help of graph-based spatial-temporal masking to explicitly model state evolution in visual RL. Specifically, we propose a self-supervised dual-component strategy that integrates (1) a graph construction of pixel-based observations for spatial-temporal masking, coupled with (2) a multilevel contrastive learning mechanism that enriches state representations by emphasizing temporal continuity and change of states. MOOSS advances the understanding of state dynamics by disrupting and learning from spatial-temporal correlations, which facilitates policy learning. Our comprehensive evaluation on multiple continuous and discrete control benchmarks shows that MOOSS outperforms previous state-of-the-art visual RL methods in terms of sample efficiency, demonstrating the effectiveness of our method.