Handed Shearing Auxetics (HSA) are a promising structure for making electrically driven robots with distributed compliance that convert a motors rotation and torque into extension and force. We overcame past limitations on the range of actuation, blocked force, and stiffness by focusing on two key design parameters: the point of an HSA's auxetic trajectory that is energetically preferred, and the number of cells along the HSAs length. Modeling the HSA as a programmable spring, we characterize the effect of both on blocked force, minimum energy length, spring constant, angle range and holding torque. We also examined the effect viscoelasticity has on actuation forces over time. By varying the auxetic trajectory point, we were able to make actuators that can push, pull, or do both. We expanded the range of forces possible from 5N to 150N, and the range of stiffness from 2 N/mm to 89 N/mm. For a fixed point on the auxetic trajectory, we found decreasing length can improve force output, at the expense of needing higher torques, and having a shorter throw. We also found that the viscoelastic effects can limit the amount of force a 3D printed HSA can apply over time.
The locomotion and mechanical efficiency of micro organisms, specifically micro-swimmers, have drawn interest in the fields of biology and fluid dynamics. A challenge in designing flagellated micro- and macro-scale robots is the geometrically nonlinear deformation of slender structures (e.g. rod-like flagella) ensuing from the interplay of elasticity and hydrodynamics. Certain types of bacteria such as Escherichia coli propel themselves by rotating multiple filamentary structures in low Reynolds flow. This multi-flagellated propulsive mechanism is qualitatively different from the single-flagellated mechanism exhibited by some other types of bacteria such as Vibrio cholerae. The differences include the flagella forming a bundle to increase directional stability for cell motility, offering redundancy for a cell to move, and offering the ability of flagella to be the delivery material itself. Above all, multi-flagellated biological system can inspire novel soft robots for application in drug transportation and delivery within the human body. We present a macroscopic soft robotic hardware platform and a computational framework for a physically plausible simulation model of the multi-flagellated robot. The fluid-structure interaction simulation couples the Discrete Elastic Rods algorithm with the method of Regularized Stokeslet Segments. Contact between two flagella is handled by a penalty-based method due to Spillmann and Teschner. We present comparison between our experimental and simulation results and verify that the simulation tool can capture the essential physics of this problem. The stability and efficiency of a multi-flagellated robot are compared with the single-flagellated counterpart.
Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Recently, it has been shown that the trajectories of iterative optimization algorithms can possess fractal structures, and their generalization error can be formally linked to the complexity of such fractals. This complexity is measured by the fractal's intrinsic dimension, a quantity usually much smaller than the number of parameters in the network. Even though this perspective provides an explanation for why overparametrized networks would not overfit, computing the intrinsic dimension (e.g., for monitoring generalization during training) is a notoriously difficult task, where existing methods typically fail even in moderate ambient dimensions. In this study, we consider this problem from the lens of topological data analysis (TDA) and develop a generic computational tool that is built on rigorous mathematical foundations. By making a novel connection between learning theory and TDA, we first illustrate that the generalization error can be equivalently bounded in terms of a notion called the 'persistent homology dimension' (PHD), where, compared with prior work, our approach does not require any additional geometrical or statistical assumptions on the training dynamics. Then, by utilizing recently established theoretical results and TDA tools, we develop an efficient algorithm to estimate PHD in the scale of modern deep neural networks and further provide visualization tools to help understand generalization in deep learning. Our experiments show that the proposed approach can efficiently compute a network's intrinsic dimension in a variety of settings, which is predictive of the generalization error.
With the goal of improving spectral efficiency, complex rotation-based precoding and power allocation schemes are developed for two multiple-input multiple-output (MIMO) communication systems, namely, simultaneous wireless information and power transfer (SWIPT) and physical layer multicasting. While the state-of-the-art solutions for these problems use very different approaches, the proposed approach treats them similarly using a general tool and works efficiently for any number of antennas at each node. Through modeling the precoder using complex rotation matrices, objective functions (transmission rates) of the above systems can be formulated and solved in a similar structure. Hence, this approach simplifies signaling design for MIMO systems and can reduce the hardware complexity by having one set of parameters to optimize. Extensive numerical results show that the proposed approach outperforms state-of-the-art solutions for both problems. It increases transmission rates for multicasting and achieves higher rate-energy regions in the SWIPT case. In both cases, the improvement is significant (20%-30%) in practically important settings where the users have one or two antennas. Furthermore, the new precoders are less time-consuming than the existing solutions.
Boolean nested canalizing functions (NCFs) have important applications in molecular regulatory networks, engineering and computer science. In this paper, we study their certificate complexity. For both Boolean values $b\in\{0,1\}$, we obtain a formula for $b$-certificate complexity and consequently, we develop a direct proof of the certificate complexity formula of an NCF. Symmetry is another interesting property of Boolean functions and we significantly simplify the proofs of some recent theorems about partial symmetry of NCFs. We also describe the algebraic normal form of $s$-symmetric NCFs. We obtain the general formula of the cardinality of the set of $n$-variable $s$-symmetric Boolean NCFs for $s=1,\dots,n$. In particular, we enumerate the strongly asymmetric Boolean NCFs.
The discovery of Behavior Trees (BTs) impacted the field of Artificial Intelligence (AI) in games, by providing flexible and natural representation of non-player characters (NPCs) logic, manageable by game-designers. Nevertheless, increased pressure on ever better NPCs AI-agents forced complexity of handcrafted BTs to became barely-tractable and error-prone. On the other hand, while many just-launched on-line games suffer from player-shortage, the existence of AI with a broad-range of capabilities could increase players retention. Therefore, to handle above challenges, recent trends in the field focused on automatic creation of AI-agents: from deep- and reinforcementlearning techniques to combinatorial (constrained) optimization and evolution of BTs. In this paper, we present a novel approach to semi-automatic construction of AI-agents, that mimic and generalize given human gameplays by adapting and tuning of expert-created BT under a developed similarity metric between source and BT gameplays. To this end, we formulated mixed discrete-continuous optimization problem, in which topological and functional changes of the BT are reflected in numerical variables, and constructed a dedicated hybrid-metaheuristic. The performance of presented approach was verified experimentally in a prototype real-time strategy game. Carried out experiments confirmed efficiency and perspectives of presented approach, which is going to be applied in a commercial game.
Promoting behavioural diversity is critical for solving games with non-transitive dynamics where strategic cycles exist, and there is no consistent winner (e.g., Rock-Paper-Scissors). Yet, there is a lack of rigorous treatment for defining diversity and constructing diversity-aware learning dynamics. In this work, we offer a geometric interpretation of behavioural diversity in games and introduce a novel diversity metric based on \emph{determinantal point processes} (DPP). By incorporating the diversity metric into best-response dynamics, we develop \emph{diverse fictitious play} and \emph{diverse policy-space response oracle} for solving normal-form games and open-ended games. We prove the uniqueness of the diverse best response and the convergence of our algorithms on two-player games. Importantly, we show that maximising the DPP-based diversity metric guarantees to enlarge the \emph{gamescape} -- convex polytopes spanned by agents' mixtures of strategies. To validate our diversity-aware solvers, we test on tens of games that show strong non-transitivity. Results suggest that our methods achieve much lower exploitability than state-of-the-art solvers by finding effective and diverse strategies.
The problem of Approximate Nearest Neighbor (ANN) search is fundamental in computer science and has benefited from significant progress in the past couple of decades. However, most work has been devoted to pointsets whereas complex shapes have not been sufficiently treated. Here, we focus on distance functions between discretized curves in Euclidean space: they appear in a wide range of applications, from road segments to time-series in general dimension. For $\ell_p$-products of Euclidean metrics, for any $p$, we design simple and efficient data structures for ANN, based on randomized projections, which are of independent interest. They serve to solve proximity problems under a notion of distance between discretized curves, which generalizes both discrete Fr\'echet and Dynamic Time Warping distances. These are the most popular and practical approaches to comparing such curves. We offer the first data structures and query algorithms for ANN with arbitrarily good approximation factor, at the expense of increasing space usage and preprocessing time over existing methods. Query time complexity is comparable or significantly improved by our algorithms, our algorithm is especially efficient when the length of the curves is bounded.
Neural waveform models such as the WaveNet are used in many recent text-to-speech systems, but the original WaveNet is quite slow in waveform generation because of its autoregressive (AR) structure. Although faster non-AR models were recently reported, they may be prohibitively complicated due to the use of a distilling training method and the blend of other disparate training criteria. This study proposes a non-AR neural source-filter waveform model that can be directly trained using spectrum-based training criteria and the stochastic gradient descent method. Given the input acoustic features, the proposed model first uses a source module to generate a sine-based excitation signal and then uses a filter module to transform the excitation signal into the output speech waveform. Our experiments demonstrated that the proposed model generated waveforms at least 100 times faster than the AR WaveNet and the quality of its synthetic speech is close to that of speech generated by the AR WaveNet. Ablation test results showed that both the sine-wave excitation signal and the spectrum-based training criteria were essential to the performance of the proposed model.
Most Deep Reinforcement Learning (Deep RL) algorithms require a prohibitively large number of training samples for learning complex tasks. Many recent works on speeding up Deep RL have focused on distributed training and simulation. While distributed training is often done on the GPU, simulation is not. In this work, we propose using GPU-accelerated RL simulations as an alternative to CPU ones. Using NVIDIA Flex, a GPU-based physics engine, we show promising speed-ups of learning various continuous-control, locomotion tasks. With one GPU and CPU core, we are able to train the Humanoid running task in less than 20 minutes, using 10-1000x fewer CPU cores than previous works. We also demonstrate the scalability of our simulator to multi-GPU settings to train more challenging locomotion tasks.
Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.