Data-driven discovery of dimensionless numbers and scaling laws from experimental measurements

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a highly-multivariable system with incomplete governing equations. In this study, we embed the principle of dimensional invariance into a two-level machine learning scheme to automatically discover dominant and unique dimensionless numbers and scaling laws from data. The proposed methodology, called dimensionless learning, can reduce high-dimensional parametric spaces into descriptions involving just a few physically-interpretable dimensionless parameters, which significantly simplifies the process design and optimization of the system. We demonstrate the algorithm by solving several challenging engineering problems with noisy experimental measurements (not synthetic data) collected from the literature. The examples include turbulent Rayleigh-Benard convection, vapor depression dynamics in laser melting of metals, and porosity formation in 3D printing. We also show that the proposed approach can identify dimensionally-homogeneous differential equations with minimal parameters by leveraging sparsity-promoting techniques

SWheg: A Wheel-Leg Transformable Robot With Minimalist Actuator Realization

This article presents the design, implementation, and performance evaluation of SWheg, a novel modular wheel-leg transformable robot family with minimalist actuator realization. SWheg takes advantage of both wheeled and legged locomotion by seamlessly integrating them on a single platform. In contrast to other designs that use multiple actuators, SWheg uses only one actuator to drive the transformation of all the wheel-leg modules in sync. This means an N-legged SWheg robot requires only N+1 actuators, which can significantly reduce the cost and malfunction rate of the platform. The tendon-driven wheel-leg transformation mechanism based on a four-bar linkage can perform fast morphology transitions between wheels and legs. We validated the design principle with two SWheg robots with four and six wheel-leg modules separately, namely Quadrupedal SWheg and Hexapod SWheg. The design process, mechatronics infrastructure, and the gait behavioral development of both platforms were discussed. The performance of the robot was evaluated in various scenarios, including driving and turning in wheeled mode, step crossing, irregular terrain passing, and stair climbing in legged mode. The comparison between these two platforms was also discussed