Design of Passive Dynamic Walking Robots for Additive Manufacture

Ongoing research in the direction of printable, non-assembly mechatronic systems give rise to the need for multi-material printing, including electronics. However, there are robotic systems that do not use electronic components and still exhibit complex dynamic behavior. Such passive dynamic systems have the potential to save energy and component cost in the field of robotics compared to actuated systems. Ongoing research in computational design synthesis of passive dynamic systems aims at automatically generating robotic configurations based on a given task. However, an automated design-to-fabrication process also requires a flexible fabrication method. Towards the goal of printing functional, non-assembly passive dynamic robots using Fused Deposition Modeling (FDM), this paper explores designing and fabricating passive walking robots and all necessary components using single material FDM. Two configurations of passive dynamic walkers are re-designed and fabricated in this paper. For one of them all components are printed in one job and only little assembly after printing is needed. However, the gait cycle of the second configuration is much more sensitive to small parametric changes and therefore more flexible prototyping is needed in order to allow adjusting of the robot after printing. Moreover, FDM printed robotic joints with sufficient smoothness and axial stiffness are required and a variety of different joint assemblies are designed and tested for the robot prototypes. Even though the most stable gait for the second robot is achieved using a metal bearing instead of the FDM printed ones, this is not necessary for the first robot example. The approach to prototyping with FDM presented in this paper allows achieving functionality through design iteration without incurring significant cost. To arrive at feasible solutions, a modular design approach allows to combine different joints, legs, feet and balancing weights and the connection points of the different elements are adjustable after printing, which makes it possible to shift the center of gravity and other variables of the robot.Mechanical Engineerin

Passive Sole Constraining Method to Stabilize 3D Passive Dynamic Walking

Inspired by the function of a toe and a lateral arch of a human foot, we propose a method to stabilize the biped walk by attaching unactuated toes and lateral arches. The toes and lateral arches work as adaptive braking of sagittal and lateral directions. They touch on the ground at the angle where the biped exceedingly inclines. After touching on the floor, the center of rotation changes at the landing positions. This change causes the reduction of the exceeding angular velocities toward sagittal and lateral directions. By setting appropriate heights of the toe and lateral arch during the swing phase, the walking robot is expected to be stabilized. To analyze the effects of the toe, we derived equations of motions and the state transition functions for a simplified 3D passive dynamic walker with toes. We clarified the potential stabilizing effect of the method from numerical simulations and preliminary experiments by a real-world biped with toes. Note that the proper setting of heights and the verification of the effect of lateral arches are on the way

Reinforcement Learning of Stable Trajectory for Quasi-Passive Dynamic Walking of an Unstable Biped Robot

Biped walking is one of the major research targets in recent humanoid robotics, and many researchers are now interested in Passive Dynamic Walking (PDW) [McGeer (1990)] rather than that by the conventional Zero Moment Point (ZMP) criterion [Vukobratovic (1972)]. The ZMP criterion is usually used for planning a desired trajectory to be tracked by

Fractal mechanism of basin of attraction in passive dynamic walking

Passive dynamic walking is a model that walks down a shallow slope without any control or input. This model has been widely used to investigate how humans walk with low energy consumption and provides design principles for energy-efficient biped robots. However, the basin of attraction is very small and thin and has a fractal-like complicated shape, which makes producing stable walking difficult. In our previous study, we used the simplest walking model and investigated the fractal-like basin of attraction based on dynamical systems theory by focusing on the hybrid dynamics of the model composed of the continuous dynamics with saddle hyperbolicity and the discontinuous dynamics caused by the impact upon foot contact. We clarified that the fractal-like basin of attraction is generated through iterative stretching and bending deformations of the domain of the Poincaré map by sequential inverse images. However, whether the fractal-like basin of attraction is actually fractal, i.e., whether infinitely many self-similar patterns are embedded in the basin of attraction, is dependent on the slope angle, and the mechanism remains unclear. In the present study, we improved our previous analysis in order to clarify this mechanism. In particular, we newly focused on the range of the Poincaré map and specified the regions that are stretched and bent by the sequential inverse images of the Poincaré map. Through the analysis of the specified regions, we clarified the conditions and mechanism required for the basin of attraction to be fractal

Modeling Framework and Software Tools for Walking Robots

In research on passive dynamic walking, the aim is to study and design robots that walk naturally, i.e., with little or no control effort. McGeer [1] and others (e.g. [2, 3]) have shown that, indeed, robots can walk down a shallow slope with no actuation, only powered by gravity.\ud In this work, we derive mathematical models of walking ro- bots to better understand the dynamics that determine the walking behavior, and to design controllers that e.g. in- crease robustness against changing environments. We use the port-Hamiltonian framework, as it has the advantage of explicitly showing energy-flows inside and into the system. Thus, it allows a direct efficiency study as well as the possi- bility to connect external elements in a ‘physical’ way using ports, instead of using just torque/force signals

Design Optimization, Analysis, and Control of Walking Robots

Passive dynamic walking refers to the dynamical behavior of mechanical devices that are able to naturally walk down a shallow slope in a stable manner, without using actuation or sensing of any kind. Such devices can attain motions that are remarkably human-like by purely exploiting their natural dynamics. This suggests that passive dynamic walking machines can be used to model and study human locomotion; however, there are two major limitations: they can be difficult to design, and they cannot walk on level ground or uphill without some kind of actuation. This thesis presents a mechanism design optimization framework that allows the designer to find the best design parameters based on the chosen performance metric(s). The optimization is formulated as a convex problem, where its solutions are globally optimal and can be obtained efficiently. To enable locomotion on level ground and uphill, this thesis studies a robot based on a passive walker: the rimless wheel with an actuated torso. We design and validate two control policies for the robot through the use of scalable methodology based on tools from mathematical analysis, optimization theory, linear algebra, differential equations, and control theory

Sudden change in fractality of basin boundary in passive dynamic walking

The 11th International Symposium on Adaptive Motion of Animals and Machines. Kobe University, Japan. 2023-06-06/09. Adaptive Motion of Animals and Machines Organizing Committee.Poster Session P7