Falling is a significant problem for older adults. It can cause severe injury and even death. Furthermore, the fear of falling has a significant influence on the life of the elderly, and therefore they reduce their physical activity. Two new balance assistive devices are being developed to reduce the risk of falling. Both devices use a control moment gyroscope (CMG) to generate a moment to counter the falling motion. One device consists of a single CMG. The other device consists of two CMGs that are coupled such that the gimbals rotate in opposite direction. This is called a scissored pair CMG (SPCMG). The purpose of this study was to examine whether it is possible to design an (SP)CMG with a passive mechanism that exploits gyroscopic precession of gimbal(s) to emulate different types of impedances for balance assistance. To examine this, first, the equations of motion of a CMG and an SPCMG were derived. Next, the equations of motion were used to derive the impedance of the system. The impedance was optimized such that it would simulate the behaviour of a spring, a damper, a mass, a mass-spring-damper system, and a rotational PD controller which is proportional to the XCoM (PDXCoM), a measure of stability. The optimization used a gradient-based algorithm to find the minimum. Multiple optimizations with different random initial guesses were performed to increase the chance to find the global minimum. Two sets of optimizations were performed.
One optimization with and one optimization without bounds on the optimization. The sets parameters that led to the best fit were used in a walking simulation to calculate the moments the device would generate during normal walking. It is shown that it is possible to simulate the dynamics of a spring, a damper, a mass, and a mass-springdamper system with a CMG and an SPCMG. However, it was not possible to replicate the dynamics of the PDXCoM with a CMG and an SPCMG. A walking simulation showed that the generated moments of the (SP)CMG were in the opposite direction of the angular velocity of the human. Therefore, using a passive mechanism to control an (SP)CMG could be used as balance assistance.

Bipedal running gaits may be self-stable if they rely on the intrinsic system dynamics to attenuate deviations. This use of passive dynamics for gait stability has been observed in biological running and applied for running robotics, supported with the results of numerical simulations. It is an important aspect of the development of fast and agile legged robotic locomotion over complex terrain. One part of running stability, trunk stabilization, can be described using a virtual pendulum model. We believe such a metacentric model may be applied in robotic design to achieve passive stabilization of body pitch for fast bipedal running.

In this study, we test metacentric models for self-stabilization of body pitch in bipedal running and evaluate the effects of running speed, design parameter variations, and control strategies. We extract data from experiments with the Planar Elliptical Runner and compare these with a planar spring-loaded inverted pendulum model with a trunk (TSLIP).

We find passive self-stable gaits in the TSLIP model with the centre of mass below the hip. These gaits demonstrate robustness to disturbances and do not require inertial measurements or high-gain feedback control. At high velocities, foot placement and choice of leg stiffness become less critical for gait stability.

Data from experiments with the Planar Elliptical Runner support the findings from the model behaviour as it runs reliably, with passively stable body pitch, and without feedback control. A metacentric model, such as the virtual pendulum model, may explain the observed passive body-pitch stabilization. Evidence from the model ground reaction forces suggests that pitch stability for the Planar Elliptical Runner can also be explained with a metacentric model. Stability in height and velocity can be explained with the compliant leg behaviour in stance.

Constructing a metacentre through mechanical design is beneficial to intrinsic body-pitch stability and subsequently facilitates full gait self-stability in fast running robotics. Implicit feedback allows off-loading of high-gain feedback control onto the system mechanical design, thus contributing to developments for fast legged locomotion over rough terrain.