Carlotta Mummolo

Quantifying Dynamic Characteristics of Human Walking for Comprehensive Gait Cycle

Normal human walking typically consists of phases during which the body is statically unbalanced while maintaining dynamic stability. Quantifying the dynamic characteristics of human walking can provide better understanding of gait principles. We introduce a novel quantitative index, the dynamic gait measure (DGM), for comprehensive gait cycle. The DGM quantifies the effects of inertia and the static balance instability in terms of zero-moment point and ground projection of center of mass and incorporates the time-varying foot support region (FSR) and the threshold between static and dynamic walking. Also, a framework of determining the DGM from experimental data is introduced, in which the gait cycle segmentation is further refined. A multisegmental foot model is integrated into a biped system to reconstruct the walking motion from experiments, which demonstrates the time-varying FSR for different subphases. The proof-of-concept results of the DGM from a gait experiment are demonstrated. The DGM results are analyzed along with other established features and indices of normal human walking. The DGM provides a measure of static balance instability of biped walking during each (sub)phase as well as the entire gait cycle. The DGM of normal human walking has the potential to provide some scientific insights in understanding biped walking principles, which can also be useful for their engineering and clinical applications.

Passive and dynamic gait measures for biped mechanism: formulation and simulation analysis

Understanding and mimicking human gait is essential for design and control of biped walking robots. The unique characteristics of normal human gait are described as passive dynamic walking, whereas general human gait is neither completely passive nor always dynamic. To study various walking motions, it is important to quantify the different levels of passivity and dynamicity, which have not been addressed in the current literature. In this paper, we introduce the initial formulations of Passive Gait Measure (PGM) and Dynamic Gait Measure (DGM) that quantify passivity and dynamicity, respectively, of a given biped walking motion, and the proposed formulations will be demonstrated for proof-of-concepts using gait simulation and analysis. The PGM is associated with the optimality of natural human walking, where the passivity weight functions are proposed and incorporated in the minimization of physiologically inspired weighted actuator torques. The PGM then measures the relative contribution of the stance ankle actuation. The DGM is associated with the gait stability, and quantifies the effects of inertia in terms of the Zero-Moment Point and the ground projection of center of mass. In addition, the DGM takes into account the stance foot dimension and the relative threshold between static and dynamic walking. As examples, both human-like and robotic walking motions during single support phase are generated for a planar biped system using the passivity weights and proper gait parameters. The calculated PGM values show more passive nature of human-like walking as compared with the robotic walking. The DGM results verify the dynamic nature of normal human walking with anthropomorphic foot dimension. In general, the DGMs for human-like walking are greater than those for robotic walking. The resulting DGMs also demonstrate their dependence on the stance foot dimension as well as the walking motion; for a given walking motion, smaller foot dimension results in increased dynamicity. Future work on experimental validation and demonstration will involve actual walking robots and human subjects. The proposed results will benefit the human gait studies and the development of walking robots.

Numerical Estimation of Balanced and Falling States for Constrained Legged Systems

Instability and risk of fall during standing and walking are common challenges for biped robots. While existing criteria from state-space dynamical systems approach or ground reference points are useful in some applications, complete system models and constraints have not been taken into account for prediction and indication of fall for general legged robots. In this study, a general numerical framework that estimates the balanced and falling states of legged systems is introduced. The overall approach is based on the integration of joint-space and Cartesian-space dynamics of a legged system model. The full-body constrained joint-space dynamics includes the contact forces and moments term due to current foot (or feet) support and another term due to altered contact configuration. According to the refined notions of balanced, falling, and fallen, the system parameters, physical constraints, and initial/final/boundary conditions for balancing are incorporated into constrained nonlinear optimization problems to solve for the velocity extrema (representing the maximum perturbation allowed to maintain balance without changing contacts) in the Cartesian space at each center-of-mass (COM) position within its workspace. The iterative algorithm constructs the stability boundary as a COM state-space partition between balanced and falling states. Inclusion in the resulting six-dimensional manifold is a necessary condition for a state of the given system to be balanced under the given contact configuration, while exclusion is a sufficient condition for falling. The framework is used to analyze the balance stability of example systems with various degrees of complexities. The manifold for a 1-degree-of-freedom (DOF) legged system is consistent with the experimental and simulation results in the existing studies for specific controller designs. The results for a 2-DOF system demonstrate the dependency of the COM state-space partition upon joint-space configuration (elbow-up vs. elbow-down). For both 1- and 2-DOF systems, the results are validated in simulation environments. Finally, the manifold for a biped walking robot is constructed and illustrated against its single-support walking trajectories. The manifold identified by the proposed framework for any given legged system can be evaluated beforehand as a system property and serves as a map for either a specified state or a specific controller’s performance.

Computational evaluation of load carriage effects on gait balance stability.

Abstract Evaluating the effects of load carriage on gait balance stability is important in various applications. However, their quantification has not been rigorously addressed in the current literature, partially due to the lack of relevant computational indices. The novel Dynamic Gait Measure (DGM) characterizes gait balance stability by quantifying the relative effects of inertia in terms of zero-moment point, ground projection of center of mass, and time-varying foot support region. In this study, the DGM is formulated in terms of the gait parameters that explicitly reflect the gait strategy of a given walking pattern and is used for computational evaluation of the distinct balance stability of loaded walking. The observed gait adaptations caused by load carriage (decreased single support duration, inertia effects, and step length) result in decreased DGM values (p < 0.0001), which indicate that loaded walking motions are more statically stable compared with the unloaded normal walking. Comparison of the DGM with other common gait stability indices (the maximum Floquet multiplier and the margin of stability) validates the unique characterization capability of the DGM, which is consistently informative of the presence of the added load.

Identification of balanced states for multi-segmental legged robots using reduced-order model

A general construction framework is introduced to provide three-dimensional balance criteria for multi-segmental legged robots. The approach is based on a reduced-order dynamic model that includes a 3-D mechanism with minimal number of degrees of freedom (DOFs) capable of representing the equivalent center-of-mass (COM) dynamics of a generic legged robot. Systematic mappings from the legged system to the reduced-order model include COM workspace, foot support region, ground reaction forces and moments, center of pressure, joint angle and actuation limits, and angular momentum. A numerical optimization algorithm is established to solve for the minimum and maximum initial COM velocity components of the 3-D mechanism that satisfy nonlinear constraints such as center of pressure boundaries, positive normal reaction, friction cone inequality, and the ability to reach a final static equilibrium. The resulting velocity extrema are the boundaries of the balanced state domain of the given legged robot, and provide the criteria of balanced versus falling state. The balanced state domain, constructed as a viability kernel, is the reachable superset of all possible controller-based domains, and represents the necessary and sufficient condition for balancing without stepping. The approach is validated for 1- and 2-DOF legged systems in sagittal plane, and applications are illustrated for a planar 4-DOF biped system.

Stability of Mina v2 for Robot-Assisted Balance and Locomotion

The assessment of the risk of falling during robot-assisted locomotion is critical for gait control and operator safety, but has not yet been addressed through a systematic and quantitative approach. In this study, the balance stability of Mina v2, a recently developed powered lower-limb robotic exoskeleton, is evaluated using an algorithmic framework based on center of mass (COM)- and joint-space dynamics. The equivalent mechanical model of the combined human-exoskeleton system in the sagittal plane is established and used for balance stability analysis. The properties of the Linear Linkage Actuator, which is custom-designed for Mina v2, are analyzed to obtain mathematical models of torque-velocity limits, and are implemented as constraint functions in the optimization formulation. For given feet configurations of the robotic exoskeleton during flat ground walking, the algorithm evaluates the maximum allowable COM velocity perturbations along the fore-aft directions at each COM position of the system. The resulting velocity extrema form the contact-specific balance stability boundaries (BSBs) of the combined system in the COM state space, which represent the thresholds between balanced and unbalanced states for given contact configurations. The BSBs are obtained for the operation of Mina v2 without crutches, thus quantifying Mina v2s capability of maintaining balance through the support of the leg(s). Stability boundaries in single and double leg supports are used to analyze the robots stability performance during flat ground walking experiments, and provide design and control implications for future development of crutch-less robotic exoskeletons.

Balanced and falling states for biped systems: Applications to robotic versus human walking stability

Designing a balance controller that allows a robot to perform human-like dynamic and stable walking is still a challenge. In this work, a recent theoretical framework for the balance stability analysis of bipeds is extended to two real multibody biped systems: a robot and a human subject. For each system in single support (SS) contact configuration, the threshold between balanced and falling state is calculated, resulting in the biped-specific balance stability boundary. This boundary identifies, in the state space of the center of mass (COM), all possible states that are balanced with respect to SS. A COM state outside of the boundary represents the sufficient condition for a falling state, from which a change in the current SS contact configuration is inevitable. The walking trajectories of both systems are analyzed in relationship with their respective stability boundary, in order to extrapolate useful implications on the different balance control of robot vs. human during the SS phase of walking. In addition, a metrics that quantifies the degree of instantaneous stability/instability is formulated, based on the relative distance from a COM state to the closest point on the stability boundary. The method and results proposed can help the improvement of current balance controllers in walking robots.

Loaded Versus Unloaded Gait Balance Stability: A Measure of Dynamic Walking

Several stability indices exist in the literature, each within their contexts and perspectives of quantification. However, no relevant index for the quantification of gait balance stability has been rigorously developed. Here, the novel Dynamic Gait Measure (DGM) is used to characterize the distinct gait balance stability of loaded walking, as compared to normal human walking. The DGM quantifies the normalized effects of inertia of a given gait with respect to the time-varying foot support region. The DGM is formulated in terms of the gait parameters reflecting a given gait strategy, and is extended to multiple steps of the gait cycle. The altered gait kinematics observed during load carriage (decreased single support duration, inertia effects, and step length) results in decreased DGM values (p < 0.0001), indicating that loaded walking is more statically stable compared with the unloaded walking. The DGM is compared with other common gait stability indices to validate its unique ability to catch the alteration (due to load carriage) in its corresponding gait stability characteristics.Copyright

Experimental analysis for passive and dynamic gait measures of biped walking

Normal human gait, described as passive dynamic walking, is neither completely passive nor always dynamic. In this article, we introduce the formulations of Passive Gait Measure (PGM) and Dynamic Gait Measure (DGM) that quantify passivity and dynamicity levels, respectively, of a given biped walking motion. The proposed concepts will be demonstrated through the analysis of human walking experimental data. The PGM measures the relative actuation contribution of the pivot joint of stance leg in the inverted pendulum analogy. The DGM, associated with gait stability, quantifies the effects of inertia in terms of the Zero-Moment Point (ZMP) and the ground projection of center of mass (GCOM). Human walking motion during single and double support phases is reconstructed from raw experimental data, and ZMP and GCOM trajectories during one full step cycle are generated. The calculated PGM values show the passive nature of human walking when the inverted pendulum analogy is adopted. The DGM results verify the dynamic nature of human walking demonstrating their dependence on the walking motion as well as the step phase; the double support phase results a static motion, opposite to the highly dynamic single support phase. The results will benefit the human gait studies and the development of walking robots.Copyright

How Dynamic is Dynamic Walking? Human vs. Robotic Gait

For design and control of biped walking robots, it is important to quantify the different level of dynamicity. We propose the Dynamic Gait Measure (DGM) that quantifies the dynamicity of a given biped walking motion. The DGM is associated with the gait stability, and quantifies the effects of inertia in terms of the Zero-Moment Point (ZMP) and the ground projection of center of mass (GCOM). Also, DGM takes into account the stance foot dimension and the relative threshold between static and dynamic walking. Human-like and robotic walking motions are generated for a planar biped system from an optimization problem. The resulting DGMs demonstrate their dependence on the stance foot dimension as well as the walking motion. The DGM results verify the dynamic nature of normal human walking. For a given gait motion, smaller foot dimension results in increased dynamicity. Moreover, the DGMs for normal human walking are greater than those for robotic walking. The proposed results will benefit the development of walking robots.Copyright