Sensing via whole-body interactions with complex terrains: physical insights from robotic models

Unlike their large-scale counterparts, small-scale robots are largely confined to laboratory environments and are rarely deployed in real-world settings. As robot size decreases, robot-terrain interactions fundamentally change; however, there remains a lack of systematic understanding of what sensory information small-scale robots should acquire and how they should respond when traversing complex natural terrains. To address these challenges, we develop a Small-scale, Intelligent, Lizard-inspired, Adaptive Robot (SILA Bot) capable of adapting to diverse substrates. We use granular media of varying depths as a controlled yet representative terrain paradigm. We show that the optimal body movement pattern (ranging from standing-wave bending that assists limb retraction on flat ground to traveling-wave undulation that generates thrust in deep granular media) can be parameterized and approximated as a linear function of granular depth. Furthermore, proprioceptive signals, such as joint torque, provide sufficient information to estimate granular depth via a K-Nearest Neighbors classifier, achieving 95% accuracy. Leveraging these relationships, we design a simple linear feedback controller that modulates body phase and substantially improves locomotion performance on terrains with unknown depth. Together, these results establish a principled framework for perception and control in small-scale locomotion and enable effective terrain-adaptive locomotion while maintaining low computational complexity.

For robots to navigate safely and efficiently on soft, granular terrains, it is crucial to gather information about the terrain's mechanical properties, which directly affect locomotion performance. Recent research has developed robotic legs that can accurately sense ground reaction forces during locomotion. However, existing tests of granular property estimation often rely on specific foot trajectories, such as vertical penetration or horizontal shear, limiting their applicability during natural locomotion. To address this limitation, we introduce a physics-informed machine learning framework, Inverse Resistive Force Theory (I-RFT), which integrates the Granular Resistive Force Theory model with Gaussian Processes to infer terrain properties from proprioceptively measured contact forces under arbitrary gait trajectories. By embedding the granular force model within the learning process, I-RFT preserves physical consistency while enabling generalization across diverse motion primitives. Experimental results demonstrate that I-RFT accurately estimates terrain properties across multiple gait trajectories and toe shapes. Moreover, we show that the quantified uncertainty over the terrain resistance stress map could enable robots to optimize foot design and gait trajectories for efficient information gathering. This approach establishes a new foundation for data-efficient characterization of complex granular environments and opens new avenues for locomotion strategies that actively adapt gait for autonomous terrain exploration.

Mechanical intelligence, loosely defined as the reduction in control burden afforded by a robot's physical form, has become a prominent concept in robotics, with instantiations in bioinspired robotics, soft robotics, robotic swarms, and many other areas. However, rigorous theoretical understanding and quantitative measures of mechanical intelligence have lagged behind the engineering systems that the community has developed. In this work, using modern legged robots as a benchmark and exemplar, we propose several information-theoretic metrics for quantifying mechanical intelligence. By viewing body dynamics as both a computational process and a communication channel, we show that several prior insights in legged-robot engineering can be described using information theory, and we quantify how bits are processed by mechanical modes and across robot coordinates. Specifically, we examine the trade-off between explicitly incorporating compliance through series-elastic actuation and using so-called proprioceptive, low-gear-ratio transmissions, and we explore how these mechanisms interact with control policies during locomotion. We develop these results on systems of increasing complexity: a simplified linear model of a robot-leg transmission, a nonlinear single-leg simulation, and simulated quadruped robots controlled by a learned policy while navigating challenging terrain. These results lay the groundwork for broader study of robot mechanisms and their role in embodied computation.