Integrating Reconfigurable Foot Design, Multi-modal Contact Sensing, and Terrain Classification for Bipedal Locomotion

The ability of bipedal robots to adapt to diverse and unstructured terrain conditions is crucial for their deployment in real-world environments. To this end, we present a novel, bio-inspired robot foot design with stabilizing tarsal segments and a multifarious sensor suite involving acoustic, capacitive, tactile, temperature, and acceleration sensors. A real-time signal processing and terrain classification system is developed and evaluated. The sensed terrain information is used to control actuated segments of the foot, leading to improved ground contact and stability. The proposed framework highlights the potential of the sensor-integrated adaptive foot for intelligent and adaptive locomotion.Comment: 7 pages, 6 figure

Oracle Complexity Classes and Local Measurements on Physical Hamiltonians

The canonical problem for the class Quantum Merlin-Arthur (QMA) is that of estimating ground state energies of local Hamiltonians. Perhaps surprisingly, [Ambainis, CCC 2014] showed that the related, but arguably more natural, problem of simulating local measurements on ground states of local Hamiltonians (APX-SIM) is likely harder than QMA. Indeed, [Ambainis, CCC 2014] showed that APX-SIM is P^QMA[log]-complete, for P^QMA[log] the class of languages decidable by a P machine making a logarithmic number of adaptive queries to a QMA oracle. In this work, we show that APX-SIM is P^QMA[log]-complete even when restricted to more physical Hamiltonians, obtaining as intermediate steps a variety of related complexity-theoretic results. We first give a sequence of results which together yield P^QMA[log]-hardness for APX-SIM on well-motivated Hamiltonians: (1) We show that for NP, StoqMA, and QMA oracles, a logarithmic number of adaptive queries is equivalent to polynomially many parallel queries. These equalities simplify the proofs of our subsequent results. (2) Next, we show that the hardness of APX-SIM is preserved under Hamiltonian simulations (a la [Cubitt, Montanaro, Piddock, 2017]). As a byproduct, we obtain a full complexity classification of APX-SIM, showing it is complete for P, P^||NP, P^||StoqMA, or P^||QMA depending on the Hamiltonians employed. (3) Leveraging the above, we show that APX-SIM is P^QMA[log]-complete for any family of Hamiltonians which can efficiently simulate spatially sparse Hamiltonians, including physically motivated models such as the 2D Heisenberg model. Our second focus considers 1D systems: We show that APX-SIM remains P^QMA[log]-complete even for local Hamiltonians on a 1D line of 8-dimensional qudits. This uses a number of ideas from above, along with replacing the "query Hamiltonian" of [Ambainis, CCC 2014] with a new "sifter" construction.Comment: 38 pages, 3 figure

Improving Foot-Mounted Inertial Navigation Through Real-Time Motion Classification

We present a method to improve the accuracy of a foot-mounted, zero-velocity-aided inertial navigation system (INS) by varying estimator parameters based on a real-time classification of motion type. We train a support vector machine (SVM) classifier using inertial data recorded by a single foot-mounted sensor to differentiate between six motion types (walking, jogging, running, sprinting, crouch-walking, and ladder-climbing) and report mean test classification accuracy of over 90% on a dataset with five different subjects. From these motion types, we select two of the most common (walking and running), and describe a method to compute optimal zero-velocity detection parameters tailored to both a specific user and motion type by maximizing the detector F-score. By combining the motion classifier with a set of optimal detection parameters, we show how we can reduce INS position error during mixed walking and running motion. We evaluate our adaptive system on a total of 5.9 km of indoor pedestrian navigation performed by five different subjects moving along a 130 m path with surveyed ground truth markers.Comment: In Proceedings of the International Conference on Indoor Positioning and Indoor Navigation (IPIN'17), Sapporo, Japan, Sep. 18-21, 201

Declutter and Resample: Towards parameter free denoising

In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth $K$ in a metric space, but it got corrupted with noise so that some of the data points lie far away from $K$ creating outliers also termed as {\em ambient noise}. One of the main goals of denoising algorithms is to eliminate such noise so that the curated data lie within a bounded Hausdorff distance of $K$. Popular denoising approaches such as deconvolution and thresholding often require the user to set several parameters and/or to choose an appropriate noise model while guaranteeing only asymptotic convergence. Our goal is to lighten this burden as much as possible while ensuring theoretical guarantees in all cases. Specifically, first, we propose a simple denoising algorithm that requires only a single parameter but provides a theoretical guarantee on the quality of the output on general input points. We argue that this single parameter cannot be avoided. We next present a simple algorithm that avoids even this parameter by paying for it with a slight strengthening of the sampling condition on the input points which is not unrealistic. We also provide some preliminary empirical evidence that our algorithms are effective in practice