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.

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.

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A theoretical–algorithmic framework for the construction of balance stability boundaries of biped robots with multiple contacts with the environment is proposed and implemented on a robotic platform. Comprehensive and univocal definitions of the states of balance of a generic legged system are introduced with respect to the system's contact configuration. Theoretical models of joint-space and center of mass (COM)-space dynamics under multiple contacts, distribution of contact wrenches, and robotic system parameters are established for their integration into a nonlinear programing (NLP) problem. In the proposed approach, the balance stability capabilities of a biped robot are quantified by a partition of the state space of COM position and velocity. The boundary of such a partition provides a threshold between balanced and falling states of the biped robot with respect to a specified contact configuration. For a COM state to be outside of the stability boundary represents the sufficient condition for falling, from which a change in the system's contact is inevitable. Through the calculated stability boundaries, the effects of different contact configurations (single support (SS) and double support (DS) with different step lengths) on the robot's balance stability capabilities can be quantitatively evaluated. In addition, the balance characteristics of the experimental walking trajectories of the robot at various speeds are analyzed in relation to their respective stability boundaries. The proposed framework provides a contact-dependent balance stability criterion for a given system, which can be used to improve the design and control of walking robots.

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 v2's capability of maintaining balance through the support of the leg(s). Stability boundaries in single and double leg supports are used to analyze the robot's stability performance during flat ground walking experiments, and provide design and control implications for future development of crutch-less robotic exoskeletons.

The human ability of keeping balance during various locomotion tasks is attributed to our capability of withstanding complex interactions with the environment and coordinating whole-body movements. Despite this, several stability analysis methods are limited by the use of overly simplified biped and foot structures and corresponding contact models. As a result, existing stability criteria tend to be overly restrictive and do not represent the full balance capabilities of complex biped systems. The proposed methodology allows for the characterization of the balance capabilities of general biped models (ranging from reduced-order to whole-body) with segmented feet. Limits of dynamic balance are evaluated by the Boundary of Balance (BoB) and the associated novel balance indicators, both formulated in the Center of Mass (COM) state space. Intermittent heel, flat, and toe contacts are enabled by a contact model that maps discrete contact modes into corresponding center of pressure constraints. For demonstration purposes, the BoB and balance indicators are evaluated for a whole-body biped model with segmented feet representative of the human-like standing posture in the sagittal plane. The BoB is numerically constructed as the set of maximum allowable COM perturbations that the biped can sustain along a prescribed direction. For each point of the BoB, a constrained trajectory optimization algorithm generates the biped’s whole-body trajectory as it recovers from extreme COM velocity perturbations in the anterior–posterior direction. Balance capabilities for the cases of flat and segmented feet are compared, demonstrating the functional role the foot model plays in the limits of postural balance. The state-space evaluation of the BoB and balance indicators allows for a direct comparison between the proposed balance benchmark and existing stability criteria based on reduced-order models [e.g., Linear Inverted Pendulum (LIP)] and their associated stability metrics [e.g., Margin of Stability (MOS)]. The proposed characterization of balance capabilities provides an important benchmarking framework for the stability of general biped/foot systems.

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Bipeds’ trajectories and control during walking are closely coupled with the contact force distribution in time and space as an indeterminate problem. Therefore, generating the motion of redundant bipeds in presence of unilateral contact is usually formulated as a nonlinear constrained optimization problem. The optimal walking motion must be solved in terms of trajectories, control, contact status (i.e., when, where, and whether a foot is in contact), and contact response (i.e., ground reaction forces). The solution for this problem requires predictive methods within the general optimal motion planning framework. However, there is a lack of fully predictive methods that can concurrently solve for all the above mentioned unknowns. This represents an important challenge in the simulation, design, analysis, and control of general robotic systems. A novel approach for the optimal motion planning of multibody systems with contacts is developed, based on a Sequential Quadratic Programming (SQP) algorithm for Nonlinear Programming (NLP). The complete formulation is presented and demonstrated with numerical experiments on a simple planar biped with the assigned task of one complete step motion in forward progression.