Optimizing Dynamic Balance in a Rat Robot via the Lateral Flexion of a Soft Actuated Spine

Abstract

Balancing oneself using the spine is a physiological alignment of the body posture in the most efficient manner by the muscular forces for mammals. For this reason, we can see many disabled quadruped animals can still stand or walk even with three limbs. This paper investigates the optimization of dynamic balance during trot gait based on the spatial relationship between the center of mass (CoM) and support area influenced by spinal flexion. During trotting, the robot balance is significantly influenced by the distance of the CoM to the support area formed by diagonal footholds. In this context, lateral spinal flexion, which is able to modify the position of footholds, holds promise for optimizing balance during trotting. This paper explores this phenomenon using a rat robot equipped with a soft actuated spine. Based on the lateral flexion of the spine, we establish a kinematic model to quantify the impact of spinal flexion on robot balance during trot gait. Subsequently, we develop an optimized controller for spinal flexion, designed to enhance balance without altering the leg locomotion. The effectiveness of our proposed controller is evaluated through extensive simulations and physical experiments conducted on a rat robot. Compared to both a non-spine based trot gait controller and a trot gait controller with lateral spinal flexion, our proposed optimized controller effectively improves the dynamic balance of the robot and retains the desired locomotion during trotting.

Figures (12)

• Figure 1: The quadruped robot tilts during trot gait. The figure of the trotting rat is cited from ham2019automated. The purple line represents the support area during trot gait, while the black point indicates the CoM of the robot. Notably, the projection of the CoM always falls outside the support area.
• Figure 2: The rat robot with a soft actuated spine. The pink line shows the soft actuated spine. The diagram in the upper right briefly illustrates that the flexing spine can be considered as a segment of a circle with a central angle $\theta_s$.
• Figure 3: Schematic of the rat robot with spinal flexion. The blue-shaded region represents the robot's skeleton in its initial state, whereas the pink-shaded region depicts the robot's skeleton when flexing its spine. $l_{HH}$ and $l_{FH}$ denote the lengths of the hind hip and fore hip, respectively. The dynamic stride lengths of the hind limb and fore limb are $l_h(t)$ and $l_f(t)$ respectively, which generate the robot's gait over time. $l_B$ is the length of the robot body. $l_S$ is the length of the spine. $R(t)$ signifies the time-varying flexing angle of the spine. $P_h$ and $P_f$ represent the footholds for the hind limb and fore limb during trotting, respectively. And the purple-shaded region connecting such two footholds presents the robot's support area. Moreover, to account for the influence of spinal flexion on the hind limb foothold, we introduce $l_{hx}(t)$ and $l_{hy}(t)$ to describe the alterations in the coordinates of the hind foothold due to spinal flexion.
• Figure 4: The distance from CoM to the support area during trotting without spinal flexion. Considering a gait stride period denoted as $T$, $dis(t)$ is calculated by (\ref{['dis']}). Referring to Fig. \ref{['fig:spine_flexion']}, when $dis(t) > 0$, CoM is on the left of $P_fP_h$ in the coordinate system, which corresponds to the right side of the support area, as indicated by the blue-shaded region. Conversely, when $dis(t) < 0$, CoM is on the left of the support area, illustrated by the pink-shaded area. The red dashed rectangle shows the results of a half period.
• Figure 5: Frontal view of the unbalanced robot. $RH$ and $LF$ are two limbs within a stance phase. The red arrow is the direction of gravity. The y-axis and z-axis are based on the local coordinate system of the robot. And $\theta_{\text{roll}}$ is the roll angle of the robot and can indicate the degree of tilt of the robot.