Biologically-inspired push recovery capable bipedal locomotion modeling through hybrid automata

Highlights

• Hybrid automata for eight stage of GAIT cycle of human is implemented.

• Design the controller for stable walk.

• Defined all the dynamic and static parameter.

• Described the domain break down of humanoid locomotion as hybrid system.

• Proposed the canonical equation for universal for moment of different join angle to produce exact human locomotion.

Abstract

The earlier developed two stage hybrid automata is not a perfect representation of human walk as it is a combination of discrete and continuous phases and the whole human GAIT has 8 stages. Our major contribution is eight stage hybrid automata for large push recovery and various dynamic parameter studies for stable walk model. We have developed a controller to verify different stage of human locomotion by using OpenSim data for model 3DGaitModel2354 and lower extremity data. We verified the hybrid automata model using the real human GAIT data for normal person. We identify the importance of the human lower extremity for locomotion and push recovery from large perturbation. The novelty of research work is to model the bipedal locomotion as a re-usable component based framework. Our original contribution lies in the fact that we have tried to view it from a software engineering perspective.

Introduction

Human like machine development in various areas is the need of the hour, for instance, in an event of disaster anthropomorphic bipedal robots can come in handy. Studying human anatomy for walking can also be utilized to design prosthetics for the injured or handicapped  [1]. The bottom line is giving the reality to the dream that robots perform tasks conducive for humans like climbing stairs, avoiding obstacles, traversing inaccessible rough terrains and space exploration are to name a few. Currently available humanoids, Honda’s Advanced Step in Innovative Mobility (ASIMO), Humanoid Robotics Project (HRP)-2 and NAO walk with bent knees so that dynamic CoM is always above the feet so that it does not roll at the cost of the flat foot move. The most evident solution to bent-knee problem seems to be purely passive walking gait without actuation. But ballistic knee dynamic walkers, similar to that of Ted McGeer’s  [2], need actuation when plying on flat surfaces, uphill or rough terrains and more importantly considering 3D, i.e. yaw effects is necessary.

To be compatible with human environment, bipeds are preferred albeit inherently unstable. Human walk is outcome of several thousands of years of evolution and thus worth this attention while most of the presently available robots walk with bent knee/flat foot  [3]. We are habitual of walking on flat ground so we are not bothered to pay attention to it. Human–robot interaction will also help in rehabilitation of injured  [4], prosthetics and assistance to elders. We develop robot capable of doing wide variety of works in place of humans. A human-inspired method for achieving bipedal robotic walking is proposed in which a hybrid model  [5] of a human is used in conjunction with experimental walking data to obtain a multi-domain hybrid system.

Humanoid locomotion modeling and generation of rhythmic pattern is considered as a highly complex and non-linear problem. There is lot of research already done in the field of bipedal locomotion. There are several methodologies which have been used to attain the insight of biped locomotion. Kiyotoshi Matsuoka  [6] has described how simple neurons can be connected together to design a neural oscillator  [7] to produce rhythmic patterns for given input parameters.

We seek to find a new way towards automatically generating stable flat ground biped robotic walking from human gait combined with human inspired control which displays a universal behavior. Human walking is realized the several DoF (Degrees of Freedom) coupled with highly non-linear dynamics and forces such that the (velocity of) leg comes to rest when it strikes the ground  [8], [9]. So we try to obtain a low dimensional representation of human walking and modeling the continuous and discrete behavior through hybrid systems  [10], [11].

The hybrid system  [12] is a dynamic system which has both continuous and discrete components. To represent such type of system we apply hybrid automata representation [13], [14]. To manifest both components, flow is represented by a differential equation while jump can be described by a difference equation or control graph allowing for more flexibility in modeling dynamic phenomena. There are several systems which can be modeled using the Hybrid systems  [15], [16], such as physical system with impact, logic-dynamic controllers, and even internet congestion to name a few  [17], [18]. In general, the state of a hybrid system  [19], [20] is defined by the values of the continuous variables and a discrete control mode [21], [22]. The state evolution is governed either, continuously according to a flow condition, or discretely according to a control graph. Continuous flow dictates, as long as so-called invariants hold true, while discrete transitions occur as soon as stated jump conditions are agreed upon  [23], [24]. Discrete transitions are associated with events also. Fig. 1, Fig. 2 are the graphical decomposition of human gait cycle into different phases.

All the earlier research related to bipedal locomotion pattern generation is classified into two categories  [25], [26]:-

• First category of bipedal walk study is based on precise knowledge about robot dynamics. The dynamics parameters are mass, location of CoM and inertia for each internal link prepared for the model. So whole study is based on the underactuated system which is very much close to human walking pattern and thus based on accuracy of model data.

• Second category of study based on the fully actuated system. On contrary this group uses very few information of dynamics such as location of total CoM and total angular momentum. This approach relies on a feed back control since controller has less information about system dynamics.

Development of system model

Before providing a formal and detailed description of our algorithm, it is necessary to provide some details into the nature of the gait cycle and the various phases associated with it. The following points summarize the relevant features of human gait  [27], [28], [29].

• Each gait cycle is usually of about 1–1.3 s on an average but the figures may vary for the given data.

• There are broadly two phases Stance and Swing and each is further into a four sub phases. Each phase and sub phase accounts for a percentage of the entire gait cycle. Usually the Swing phase roughly accounts for 40% of the gait cycle and Stance phase approximates to 60% of the gait cycle.

They are further subdivided as follows in Table 1:

These timestamps are not very sharp and distinct that is, in other words the decision boundaries between the different sub phases have an inherent fuzziness associated with them  [30]. There might be missing timestamps and other data points in the training dataset  [31], hence the system was first trained on a rigorous human annotated and almost error free standard dataset  [32], [33]. Subsequently other datasets were added to it in order to enrich it. As mentioned before the sampling rate of the data plays a very important role, as under sampling as well as oversampling require minor tweaking of our algorithm.

The phases of the human gait are depicted in Fig. 3:

Physical observation of human gait[]

• The motion of the COM is sinusoidal in nature both in the vertical and the horizontal plane.

• The two phases occur alternately, that is when one leg is in swing phase the other leg is in the stance phase and vice-versa.

• The Gait signal is unique to a given person but the phases and their response time in general are almost common to all persons.

• This periodicity in gait signal has to be exploited in order to achieve tangible results.

• The motion signal of the knee is highly non-linear due a double hump which is noticed in the knee signal. This makes things much more difficult to model. All the difficulty arises from this non-linear signal.

The organization of the paper is divided into six sections. Section  1 gives the essential background details, history, terminology of hybrid system and human locomotion modeled as a hybrid automaton. Section  2 is dedicated to the Human GAIT analysis, which is essentially a foremost requirement for discernment of human locomotion, their stability analysis and their capability of recovering from unknown perturbations. Section  3 is dedicated for hybrid system and manifestation as hybrid automata. Section  4 is about the humanoid locomotion as hybrid system and the parameters for hybrid automata design. The fifth section is verification of our hybrid automata model with OpenSim humanoid gait data  [34]. The last section will tell about more the concluding remarks and future scope with impending work.