Efficient, Responsive, and Robust Hopping on Deformable Terrain (2311.18685v2)

Abstract: Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid substrates. In this study we focus on the ramifications of plastic terrain deformation on the hop-to-hop energy dynamics of a spring-legged monopedal hopping robot animated by a switched-compliance energy injection controller. From this deliberately simple robot-terrain template, we derive a hop-to-hop energy return map, and we use physical experiments and simulations to validate the hop-to-hop energy map for a real robot hopping on a real deformable substrate. The dynamical properties (fixed points, eigenvalues, basins of attraction) of this map provide insights into efficient, responsive, and robust locomotion on deformable terrain. Specifically, we identify constant-fixed-point surfaces in a controller parameter space that suggest it is possible to tune control parameters for efficiency or responsiveness while targeting a desired gait energy level. We also identify conditions under which fixed points of the energy map are globally stable, and we further characterize the basins of attraction of fixed points when these conditions are not satisfied. We conclude by discussing the implications of this hop-to-hop energy map for planning, control, and estimation for efficient, agile, and robust legged locomotion on deformable terrain.

• The paper demonstrates that controlled energy injection through virtual leg adjustments compensates for energy loss due to terrain deformation.
• The study maps hop-to-hop kinetic energy dynamics using drop-jump experiments with a two-mass robot model on a granular medium.
• The research offers actionable insights into controller parameters that enhance efficiency and stability for legged robots on challenging terrains.

Understanding Hopping Robot Locomotion on Deformable Surfaces

The Challenge of Deformable Terrain

One of the principal challenges in robotics is enabling legged robots to traverse uneven and deformable surfaces. Such capability is critical for applications ranging from disaster response and exploration to agriculture and environmental restoration. A significant issue that arises is the loss of energy caused by terrain deformation, which can hinder a robot's locomotion efficiency.

A Focus on Monopedal Hoppers

Researchers have focused on a minimalistic robot model, the monopedal hopper, to delve into the interaction between a robot's movements and the changing terrain beneath it. A monopedal hopper is a one-legged robot that can offer insights into more complex legged systems due to the simplicity of its design and interactions with the environment.

Injection of Energy and Stability

For legged locomotion to be sustained, robots must replace energy lost in each step. This is where controllers that govern the robot's behavior come into play. A particular type of controller, inspired by previous work on rigid surfaces, is utilized, which injects energy into the robot through updates in the stiffness and length of its virtual leg spring during the stance phase—the moment when the leg is in contact with the ground.

Energy Dynamics and Plastic Terrain Deformation

The paper examines the hop-to-hop energy dynamics on deformable terrain and how reyields, or additional terrain deformations that occur when the ground cannot withstand the force exerted by the robot, affect these dynamics. To investigate this, researchers developed a map that tracked the kinetic energy of the robot from one hop to the next, considering both the energy injected by the robot onto itself and the energy dissipated through terrain deformation.

Experimentation and Mapping

To validate the theoretical framework, a series of drop-jump experiments were conducted using a two-mass vertically-constrained robot and a controlled bed of granular material. The outcome of these experiments was consistent with the predicted map dynamics, providing confidence in the model’s applicability to real-world scenarios.

Insights into Efficiency and Responsiveness

The energy map has revealed vital dynamics which inform both the efficiency – the ability to minimize energy use – and responsiveness, here represented as the stability margin of the robot's gait. By detailing how various control parameters impact these qualities, the research offers a roadmap toward fine-tuning robotic locomotion for traversing complex and unpredictable terrains.

Future Applications

The insights gained from this work have significant implications for the future of robotic movement on deformable surfaces. As we get better at understanding and controlling legged locomotion on such substrates, robots will become increasingly capable of handling the varied and challenging terrains they will encounter in real-world missions. The development of legged robots that can traverse these surfaces effectively has broad-reaching implications for many sectors, pointing towards a future where robots can go almost anywhere that humans can, and beyond.

This paper bridges a gap in robotic locomotion and opens up new avenues for designing legged robots that can confidently step into a future cluttered with challenging terrains.