Centroidal Moment Pivot Research Articles

Centroidal Moment Pivot for ambulatory estimation of relative feet and CoM movement post stroke: Portable Gait Lab.

Measuring gait and balance recovery is necessary post stroke. In an earlier study, we developed a minimal three Inertial Measurement Units (IMUs) system called Portable Gait Lab (PGL). The PGL used the Centroidal Moment Pivot (CMP) assumption to estimate relative foot and centre of mass (CoM) positions, and thereby estimate gait parameters in healthy participants. In this study, we validate the feasibility of the PGL to track foot and CoM trajectory during gait in four persons with chronic stroke. Spatiotemporal gait and balance measures were estimated from the foot and CoM trajectories, and compared with the reference ForceShoes™. Each participant made at least 20 steps, and the PGL was able to track foot and CoM trajectories with a root mean square of the differences with the reference of 2.9 ± 0.2 cm and 4.6 ± 3.6 cm. The distances between either foot at the end of the walking task, and step lengths were estimated by PGL with an average error with the reference of 1.98 ± 2.2 cm and 7.8 ± 0.1 cm respectively across participants. We show that our approach was able to estimate spatiotemporal and balance parameters related to gait quality in a clinically useful manner. We recommend conducting further studies to study the feasibility of using the PGL system for variable gait patterns measured post stroke.

Whole-body momentum control with linear quadratic state incremental walking pattern generation and a centroidal moment pivot balancing strategy for humanoid robots

ABSTRACT In this paper, a proposed momentum control framework adopts the quadratic programming method to handle the multi-task prioritized problem by assigning suitable constraints and the objective function, including desired end-effectors motions, the limitations of joints and the rate of change of linear and angular momentum of a robot. First, the centroidal momentum matrix is used to derive the relationship between the linear and angular momentum of the center of mass and the whole-body motion of the robot. Second, the linear quadratic state incremental walking pattern generator is used to regulate the rate of change of linear momentum of the robot for balanced walking. Then, according to the difference between the centroidal moment pivot and the zero moment point (ZMP), the compensatory rate of change of horizontal angular momentum can be calculated to keep the balance from unexpected larger disturbances. Finally, the performance of this control framework is verified effectively through the simulations and the experiments. In addition, the ZMP tracking performance is improved up to 50% in the simulations and 14% in the experiments.

Balance Stability Augmentation for Wheel-Legged Biped Robot Through Arm Acceleration Control

A self-balancing wheel-legged robot provides higher maneuverability and mobility than legged biped robots. For this reason, wheel-legged systems have attracted enormous interest from academia and commercial sectors in recent years. Most of the past works in this field mainly focused on lower body stabilization. Motivated by the human ability to maintain balance in laborious activities by articulating the arm actively, we explore and analyze the active arm control on top of the wheel-legged system to assist in its balance recovery during external pushes and disturbances. This paper presents a control framework to improve the stability and robustness of an underactuated self-balancing wheel-legged robot using its upper limb arm. Furthermore, we use the centroidal moment pivot (CMP) as a key metric to quantitatively evaluate the effect of the active arm usage on the balance stability improvement of the robot in the ROS-Gazebo environment. The difference from the case of nonusage of arm is verified to clarify the impact of the active arm quantitatively. This concept would lead to the wheel-legged biped robot with an active arm for dual purposes, one is for carrying objects, another is for increasing the balance stability. This point is important for future application in a real-world environment with human-robot interactions.

Portable Gait Lab: Tracking Relative Distances of Feet and CoM Using Three IMUs.

Ambulatory estimation of gait and balance parameters requires knowledge of relative feet and centre of mass (CoM) positions. Inertial measurement units (IMU) placed on each foot, and on the pelvis are useful in tracking these segments over time, but cannot track the relative distances between these segments. Further, drift due to strapdown inertial navigation results in erroneous relative estimates of feet and CoM positions after a few steps. In this study, we track the relative distances using the assumptions of the Centroidal Moment Pivot (CMP) theory. An Extended Kalman filter approach was used to fuse information from different sources: strapdown inertial navigation, commonly used constraints such as zero velocity updates, and relative segment distances from the CMP assumption; to eventually track relative feet and CoM positions. These estimates were expressed in a reference frame defined by the heading of each step. The validity of this approach was tested on variable gait. The step lengths and step widths were estimated with an average absolute error of 4.6±1.5 cm and 3.8±1.5 cm respectively when compared against the reference VICON©. Additionally, we validated the relative distances of the feet and the CoM, and further, show that the approach proves useful in identifying asymmetric gait patterns. We conclude that a three IMU approach is feasible as a portable gait lab for ambulatory measurement of foot and CoM positions in daily life.

Closed-loop push recovery for inexpensive humanoid robots

Active balancing in autonomous humanoid robots is a challenging task due to the complexity of combining a walking gait with dynamic balancing, vision and high-level behaviors. Humans not only walk successfully over even and uneven terrain, but can recover from the interaction of external forces such as impacts with obstacles and active pushes. While push recovery has been demonstrated successfully in, expensive robots, it is more challenging with robots that are inexpensive, with limited power in actuators and less accurate sensing. This work describes a closed-loop feedback control method that uses an accelerometer and gyroscope to allow an inexpensive humanoid robot to actively balance while walking and recover from pushes. Three common balancing strategies: center of pressure, centroidal moment pivot, and step-out, for biped robots are studied. An experiment is performed to test three hand-tuned closed-loop feedback control configurations; using only the gyroscope, only the accelerometer, and a combination of both sensors to recover from pushes. Each of the sensors is discretized into four discrete domains in order to categorize pushes with different strengths. Experimental results show that the combination of gyroscope and accelerometer outperforms the other methods with 100% recovery from a light push and 70% recovery from a strong push. The proposed closed-loop feedback control is examined in both simulation and real-world.

Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion

In this paper, the concept of divergent component of motion (DCM, also called “Capture Point”) is extended to 3-D. We introduce the “Enhanced Centroidal Moment Pivot point” (eCMP) and the “Virtual Repellent Point” (VRP), which allow for the encoding of both direction and magnitude of the external forces and the total force (i.e., external plus gravitational forces) acting on the robot. Based on eCMP, VRP, and DCM, we present methods for real-time planning and tracking control of DCM trajectories in 3-D. The basic DCM trajectory generator is extended to produce continuous leg force profiles and to facilitate the use of toe-off motion during double support. The robustness of the proposed control framework is thoroughly examined, and its capabilities are verified both in simulations and experiments.

Angular momentum in human walking

Angular momentum is a conserved physical quantity for isolated systems where no external moments act about a body's center of mass (CM). However, in the case of legged locomotion, where the body interacts with the environment (ground reaction forces), there is no a priori reason for this relationship to hold. A key hypothesis in this paper is that angular momentum is highly regulated throughout the walking cycle about all three spatial directions [|Lt| approximately 0], and therefore horizontal ground reaction forces and the center of pressure trajectory can be explained predominantly through an analysis that assumes zero net moment about the body's CM. Using a 16-segment human model and gait data for 10 study participants, we found that calculated zero-moment forces closely match experimental values (Rx2=0.91; Ry2=0.90). Additionally, the centroidal moment pivot (point where a line parallel to the ground reaction force, passing through the CM, intersects the ground) never leaves the ground support base, highlighting how closely the body regulates angular momentum. Principal component analysis was used to examine segmental contributions to whole-body angular momentum. We found that whole-body angular momentum is small, despite substantial segmental momenta, indicating large segment-to-segment cancellations ( approximately 95% medio-lateral, approximately 70% anterior-posterior and approximately 80% vertical). Specifically, we show that adjacent leg-segment momenta are balanced in the medio-lateral direction (left foot momentum cancels right foot momentum, etc.). Further, pelvis and abdomen momenta are balanced by leg, chest and head momenta in the anterior-posterior direction, and leg momentum is balanced by upper-body momentum in the vertical direction. Finally, we discuss the determinants of gait in the context of these segment-to-segment cancellations of angular momentum.