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1. Variable Binding for Sparse Distributed Representations: Theory and Applications

   https://doi.org/10.1109/TNNLS.2021.3105949  

   Frady, Edward Paxon ; Kleyko, Denis ; Sommer, Friedrich T. ( September 2021 , IEEE Transactions on Neural Networks and Learning Systems)

   Variable binding is a cornerstone of symbolic reasoning and cognition. But how binding can be implemented in connectionist models has puzzled neuroscientists, cognitive psychologists, and neural network researchers for many decades. One type of connectionist model that naturally includes a binding operation is vector symbolic architectures (VSAs). In contrast to other proposals for variable binding, the binding operation in VSAs is dimensionality-preserving, which enables representing complex hierarchical data structures, such as trees, while avoiding a combinatoric expansion of dimensionality. Classical VSAs encode symbols by dense randomized vectors, in which information is distributed throughout the entire neuron population. By contrast, in the brain, features are encoded more locally, by the activity of single neurons or small groups of neurons, often forming sparse vectors of neural activation. Following Laiho et al. (2015), we explore symbolic reasoning with a special case of sparse distributed representations. Using techniques from compressed sensing, we first show that variable binding in classical VSAs is mathematically equivalent to tensor product binding between sparse feature vectors, another well-known binding operation which increases dimensionality. This theoretical result motivates us to study two dimensionality-preserving binding methods that include a reduction of the tensor matrix into a single sparse vector. One bindingmore »method for general sparse vectors uses random projections, the other, block-local circular convolution, is defined for sparse vectors with block structure, sparse block-codes. Our experiments reveal that block-local circular convolution binding has ideal properties, whereas random projection based binding also works, but is lossy. We demonstrate in example applications that a VSA with block-local circular convolution and sparse block-codes reaches similar performance as classical VSAs. Finally, we discuss our results in the context of neuroscience and neural networks.« less
2. Convex Optimization for Spring Design of Parallel Elastic Actuators

   Guo, S. ; Gregg, R. ; Bolivar-Nieto, E. ( January 2022 , Proceedings of the American Control Conference)

   Elastic actuation can improve human-robot interaction and energy efficiency for wearable robots. Previous work showed that the energy consumption of series elastic actuators can be a convex function of the series spring compliance. This function is useful to optimally select the series spring compliance that reduces the motor energy consumption. However, series springs have limited influence on the motor torque, which is a major source of the energy losses due to the associated Joule heating. Springs in parallel to the motor can significantly modify the motor torque and therefore reduce Joule heating, but it is unknown how to design springs that globally minimize energy consumption for a given motion of the load. In this work, we introduce the stiffness design of linear and nonlinear parallel elastic actuators via convex optimization. We show that the energy consumption of parallel elastic actuators is a convex function of the spring stiffness and compare the energy savings with that of optimal series elastic actuators. We analyze robustness of the solution in simulation by adding uncertainty of 20% of the RMS load kinematics and kinetics for the ankle, knee, and hip movements for level-ground human walking. When the winding Joule heating losses are dominant withmore »respect to the viscous losses, our optimal PEA designs outperform SEA designs by further reducing the motor energy consumption up to 63%. Comparing to the linear PEA designs, our nonlinear PEA designs further reduced the motor energy consumption up to 31%. From our convex formulation, our global optimal nonlinear parallel elastic actuator designs give two different elongation-torque curves for positive and negative elongation, suggesting a clutching mechanism for the final implementation. In addition, the different torque-elongation profiles for positive and negative elongation for nonlinear parallel elastic actuators can cause sensitivity of the energy consumption to changes in the nominal load trajectory.« less
3. Convex Optimization for Spring Design in Series Elastic Actuators: From Theory to Practice

   https://doi.org/10.1109/IROS51168.2021.9636427  

   Bolivar-Nieto, Edgar A. ; Thomas, Gray C. ; Rouse, Elliott ; Gregg, Robert D. ( September 2021 , 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   Natural dynamics, nonlinear optimization, and, more recently, convex optimization are available methods for stiffness design of energy-efficient series elastic actuators. Natural dynamics and general nonlinear optimization only work for a limited set of load kinetics and kinematics, cannot guarantee convergence to a global optimum, or depend on initial conditions to the numerical solver. Convex programs alleviate these limitations and allow a global solution in polynomial time, which is useful when the space of optimization variables grows (e.g., when designing optimal nonlinear springs or co-designing spring, controller, and reference trajectories). Our previous work introduced the stiffness design of series elastic actuators via convex optimization when the transmission dynamics are negligible, which is an assumption that applies mostly in theory or when the actuator uses a direct or quasi-direct drive. In this work, we extend our analysis to include friction at the transmission. Coulomb friction at the transmission results in a non-convex expression for the energy dissipated as heat, but we illustrate a convex approximation for stiffness design. We experimentally validated our framework using a series elastic actuator with specifications similar to the knee joint of the Open Source Leg, an open-source robotic knee-ankle prosthesis.
4. Resonator Networks, 1: An Efficient Solution for Factoring High-Dimensional, Distributed Representations of Data Structures

   https://doi.org/https://doi.org/10.1162/neco_a_01331  

   Frady, E. Paxon ; Kent, Spencer J. ; Olshausen, Bruno A. ; Sommer, Friedrich ( December 2020 , Neural computation)

   The ability to encode and manipulate data structures with distributed neural representations could qualitatively enhance the capabilities of traditional neural networks by supporting rule-based symbolic reasoning, a central property of cognition. Here we show how this may be accomplished within the framework of Vector Symbolic Architectures (VSAs) (Plate, 1991; Gayler, 1998; Kanerva, 1996), whereby data structures are encoded by combining high-dimensional vectors with operations that together form an algebra on the space of distributed representations. In particular, we propose an efficient solution to a hard combinatorial search problem that arises when decoding elements of a VSA data structure: the factorization of products of multiple codevectors. Our proposed algorithm, called a resonator network, is a new type of recurrent neural network that interleaves VSA multiplication operations and pattern completion. We show in two examples—parsing of a tree-like data structure and parsing of a visual scene—how the factorization problem arises and how the resonator network can solve it. More broadly, resonator networks open the possibility of applying VSAs to myriad artificial intelligence problems in real-world domains. The companion article in this issue (Kent, Frady, Sommer, & Olshausen, 2020) presents a rigorous analysis and evaluation of the performance of resonator networks, showing itmore »outperforms alternative approaches.« less
5. Self-locking origami structures and locking-induced piecewise stiffness

   https://doi.org/10.1115/DETC2017-67197  

   Fang, Hongbin ; Chu, Shih-Cheng A. ; and Wang, K.W. ( January 2017 , ASME section IX)

   The folding motion of an origami structure can be stopped at a non-flat position when two of its facets bind together. Such facet-binding will induce self-locking so that the overall origami structure can stay at a pre-specified configuration without the help of additional locking devices or actuators. This research investigates the designs of self-locking origami structures and the locking-induced kinematical and mechanical properties. We show that incorporating multiple cells of the same type but with different geometry could significantly enrich the self-locking origami pattern design. Meanwhile, it offers remarkable programmability to the kinematical properties of the selflocking origami structures, including the number and position of locking points, and the deformation range. Self-locking will also affect the mechanical characteristics of the origami structures. Experiments and finite element simulations reveal that the structural stiffness will experience a sudden jump with the occurrence of self-locking, inducing a piecewise stiffness profile. The results of this research would provide design guidelines for developing self-locking origami structures and metamaterials with excellent kinematical and stiffness characteristics, with many potential engineering applications.