Walking Robots

Abstract

This article presents an overview of mobile “walking” robots that use their legs to move from one place to another. Walking robots represent a fascinating class of machines which holds the potential for breakthrough applications and inspires multidisciplinary research with rich scientific content. The key feature that separates walking robots from all other classes of mobile robots is their ability to explore unprepared surfaces using discrete footholds. In this respect, these robots are truly the machine counterparts of biological land animals.

Introduction

The adventure of modern robotics is generally considered to have started from the middle of the twentieth century (International Federation of Robotics 2011). During the first few decades of this new journey, robots were not mobile. Somewhat similar to trees, these so-called “arm” manipulator robots were securely rooted to the ground. The free end of these robots typically consisted of an end-effector “hand” with which a number of mostly manufacturing-related tasks, such as welding, spray-painting, and pick-and-place operations, were performed. Life was simple, if a bit boring. However, from the end of the 1960s, this started to change.

Fiction writers had earlier imagined a variety of mobile robots such as in “I, Robot” (Asimov 1950), Otho (Hamilton 1940), and Maria (:̧def :̧def Malone 2004). Scientists and engineers also ventured to build a number of quite sophisticated machines such as the General Electric experimental “walking truck” quadruped robot by Mosher shown in Fig. 1 and the Sparko and Elektro by Westinghouse (http://en.wikipedia.org/wiki/Elektro). However, they were not considered truly autonomous in the sense we describe modern robots. Some of the major personalities who are primarily responsible for forever transforming the state of stationary existence of robots and giving them intelligent mobility are Profs. I. Kato, M. Vukobratovic, and R. McGhee, followed by Prof. M. Raibert.

Walking Robots, Fig. 1

GE “walking truck” developed by Mosher

Because walking robots used legs for locomotion, they immediately became the mechatronic cousins to the entire range of biological legged creatures, starting from tiny creatures to large animals. Indeed, today we have robotic versions of spiders and cockroaches, geckoes and lizards, dogs and cheetah, and even humanoids. We have seen very large robots such as the ASV (Waldron and McGhee 1986) shown in Fig. 2 and the Dante (Bares and Wettergreen 1999), shown in Fig. 4. We have also seen single-legged robots, which even Mother Nature has not considered creating so far.

Walking Robots, Fig. 2

Adaptive suspension vehicle (ASV), Ohio State University

Early History

The early researchers whom we mentioned above started paving the way for walking robots. These robots walked with their legs, explored their own environments, and sometimes even ventured outside. Once these walking robots started appearing on the scene, life was never the same.

Prof. Kato pioneered walking robot research at Waseda University (Japan) through a series of remarkable biped humanoid robots, of which WL-5 is credited with genuine bipedal walking and WL-6 with displaying the first dynamic gait. At the same time, Prof. Vukobratovic was conducting research activities in exoskeleton and other areas at the Mihailo Pupin Institute (former Yugoslavia). He was instrumental in formalizing the concept of dynamic balance using the zero moment point (ZMP) concept (Sardain and Bessonnet 2004; Vukobratović and Juričić 1969), which is used to this day. In the USA, Prof. McGhee conducted path-breaking research on computer-controlled machines at the Ohio State University. He created the Ohio hexapod and later, with colleague Prof. Ken Waldron, developed the truly spectacular Adaptive Suspension Vehicle (ASV) hexapod.

Prof. Raibert started building robots in the USA, first at Carnegie Mellon University and then at Massachusetts Institute of Technology (Raibert 1989). With his colleagues, he created a series of robots, which, unlike their stationary predecessors, were characteristically full of energy. Situation permitting, they would occasionally deviate from conventional walking and running and would burst into aerial somersaults and other acrobatic motions. Prof. Raibert continues to actively shape the field of walking robots to the present day; his company Boston Dynamics (recently acquired by Google Inc.) has introduced a number of high-performance robots, such as LittleDog, BigDog, RHex, Petman, and Atlas.

The hardware, sensing, and control aspects of walking robots were steadily gaining sophistication during the 1990s. However, except for the new appreciation of walking dynamics in the study of passive bipedal gait (McGeer 1990), there was no unexpected leap in the world of walking robots. This changed in 1996 when Honda publicly announced the humanoid robot P2, the result of their robotics project, till then unknown to the outside world. This was to be superseded by the P3 robot and then the ASIMO humanoid robot project in 2000, which became another important event in the humanoid robot history.

Characteristics of Walking Robots

Compared to other forms of land locomotion, legged walking possesses the distinct capability of locomotion using discrete footholds (Raibert 1989). Unlike wheeled mobile robots or cars, walking robots do not need a continuous prepared surface such as paved road, trail, or track in order to travel. By virtue of this single feature, a vast extent of land surface, which is not accessible to wheeled robots, opens up to walking robots. Indeed, at least in principle, walking robots are able to reach almost any location, on earth and on other planets, wherever human and other legged creatures can go.

Legged locomotion is natural to terrains where the only means of locomotion must be through the use of unstructured footholds, which can be irregularly spaced both horizontally and vertically. Due to the unique design of the leg, legged creatures can largely isolate the “payload” or the upper body from the geometric details of the terrain profile during locomotion. Both for biological creatures and for walking robots, this brings benefit in the form of significant energy savings. For walking robots this also reduces mechanical stress, vibration, and wear on the system hardware, which makes them suitable for locomotion in rough natural terrain.

In contrast, wheeled robots are typically faster, mechanically less complex, and energetically more efficient. However, these benefits must be supported by very expensive infrastructure overhead. In many places such expenditure is not practical or not even desirable.

Classification of Walking Robots

Walking robots have been built in different sizes and morphologies. These robots have ranged in sizes from small hexapods (Lewinger et al. 2005), medium-sized robots (Fig. 4), and relatively large robots such as the BigDog (Raibert et al. 2008) from Boston Dynamics and Toyota iWalk (Fig. 4) and also a few giant robots such as Dante (Bares and Wettergreen 1999) and Ambler (Fig. 4) from CMU and the ASV (Waldron and McGhee 1986) from OSU. With further miniaturization, it is conceivable that we will see even smaller walking robots in the future with unanticipated and surprising application domains. One can also imagine gigantic walking robots in potential applications in large construction sites such as in bridge, building, or ships, but we have not started seeing them just yet.

In terms of the number of legs, we have already seen monopods, Figs. 3b and 4a; bipeds, Fig. 8a–c; tripod, Fig. 4b; quadruped, Fig. 4a, b; hexapods, Figs. 4c, d and 2; octopod, Fig. 4e; and “centipede” robots with many legs, Fig. 4f.

Walking Robots, Fig. 3

Early walking robots: (a) Waseda WL-10 (Image courtesy Atsuo Takanishi) and (b) one-legged robot (Image courtesy of Boston dynamics)

Walking Robots, Fig. 4

Walking robots with different number of legs: (a) monopod, Toyota hopping robot; (b) tripod, STriDER, RoMeLa (Image courtesy of Dennis Hong); (c) large hexapod, McGhee, OSU; (d) RHex (RHex robot image courtesy of Boston Dynamics); (e) octopod, Spider, RoMeLa (Image courtesy of Dennis Hong); and (f) many legs, centipede, Harvard

Walking Robots, Fig. 5

Two quadruped robots: (a) Sony Aibo (Image courtesy of Sony) and (b) BigDog robot (Image courtesy of Boston Dynamics)

Walking Robots, Fig. 6

Large walking robots: (a) Dante II, CMU; (b) Ambler, CMU; and (c) John Deere Walking Tractor

Other than monopods, robots with odd-numbered legs are curiously absent in this list. Creatures with odd-numbered legs are also not found in nature. It is not clear if an engineering rationale is present behind this trend or the biological inspiration is simply missing for the creators of legged robots.

In addition to size and morphology, walking robots can be classified in terms of the number and types of leg joints, type of gait (e.g., walking or running), or the domain of movement. The next section is devoted to the humanoid robots, which is perhaps the most popular class of walking robots.

Humanoid Robots

Humanoid robots belong to a unique class of two-legged walking robots that has a special place in the popular psyche. These robots are the subject of special affection and fascination due to their similarity with human beings. In fact, humanoid robots might be the original inspiration behind the entire field of robotics and perhaps also its ultimate goal. Being perpetually inspired by movies and novels, a long-standing dream of the human has been to create a mechatronic replica of themselves, the human, which will be fully general-purpose endowed with all human functionalities except perhaps the full independence of thought and action.

Humanoid robots exist in different sizes, including smaller robots such as NAO (Gouaillier et al. 2009), HOAP, and QRIO (Ishida et al. 2004) and life-sized robots such as HRP, HUBO, and ASIMO. Despite their differences, these robots bear a close resemblance to the kinematic design and proportions of a human being and share a common human-mimicking morphology. Indeed, the perceived similarity between humanoid robots and the human is so close that we routinely describe aspects of such robots using anthropomorphic terms. Terms like head, arm, hand, leg, thigh, shank, ankle, spine, gait, stumble, fall, facial expression, and even emotion are hardly ever used to describe any other man-made device. Some popular humanoid robots are shown in Fig. 9.

At current technical level, humanoid robots cannot compete in their actual utility with robots such as Roomba the vacuum cleaner, the bomb-sniffing robot, or the huge population of fully active and cost-effective welding and spray-painting robots. Yet, our fascination with humanoids remains as strong as ever, and novel applications of such robots are continuously being explored (Fig. 7). Humanoid robots are currently considered in roles of educators (Falconer 2013; Yamasaki and Nakagawa 2006), dance partners (Kosuge 2010), waiters, babysitters, companions for autistic children or for seniors (Robins et al. 2012), security, or emergency response team. Curiously, the functionality of walking is not relevant or central to many of these roles.

Walking Robots, Fig. 7

Novel application of walking robots: human-carrying “chair” robots, (a) iWalk of Toyota and (b) WL-16RV multi-purpose biped locomotor from Waseda University (Image courtesy of Atsuo Takanishi)

Walking Robots, Fig. 8

Two well-known human-sized humanoid robots: (a) ASIMO, Honda. (b) HRP-2, AIST (Image courtesy of AIST). (c) HUBO, Korea

Walking Robots, Fig. 9

Three popular humanoid robots: (a) AIST HRP-4 (Image courtesy of AIST), (b) Toyota Partner Robot, and (c) Waseda University Wabian (Image courtesy of Atsuo Takanishi)

Walking Robots, Fig. 10

Three small humanoid robots: Aldebaran NAO (Image courtesy of Aldebaran), Fujitsu HOAP-2, and Sony QRIO (Image courtesy of Sony)

Dynamic Equations of Walking Robots

The dynamic equations of a walking robot can be expressed in the following form:

$$\displaystyle{ \mathbf{H}(\mathbf{q})\,\ddot{\mathbf{q}} + \mathbf{C}(\mathbf{q},\dot{\mathbf{q}})\,\dot{\mathbf{q}} +\boldsymbol{\tau } _{g}(\mathbf{q}) =\boldsymbol{\varGamma } +\boldsymbol{\varGamma }_{c} +\boldsymbol{\varGamma } _{\mathrm{ext}}, }$$

(1)

where $\mathbf{q}$ is the vector of the robot’s generalized coordinates, which contains the world frame transformation matrix of its base link and all its joint angles. The generalized velocity vector is expressed as $\dot{\mathbf{q}} = [\mathbf{v}_{B}\ \ \ \dot{\boldsymbol{\theta }}]^{T}$ where $\mathbf{v}_{B}$ is the base velocity and $\dot{\boldsymbol{\theta }}$ is the vector of joint velocities. Additionally, $\mathbf{H}$ is the joint-space inertia matrix; $\mathbf{C}$ is the matrix of Coriolis, centrifugal, and gyroscopic terms; and $\boldsymbol{\tau }_{g}$ is the vector of gravity terms. Finally, $\boldsymbol{\varGamma }= [\mathbf{0}\ \ \boldsymbol{\tau }]^{T}$ is the joint torque vector, $\boldsymbol{\varGamma }_{c} = \mathbf{J}_{c}^{T}\mathbf{f}_{c}$ is the joint torque resulting from the contact forces $\mathbf{f}_{c}$ such as from the ground, and $\boldsymbol{\varGamma }_{\mathrm{ext}} = \mathbf{J}_{e}^{T}\mathbf{f}_{e}$ is the joint torque due to external interaction forces $\mathbf{f}_{e}$.

The contact conditions which the robot must satisfy can be written in the form of Eq. 2. The physical constraints due to ground friction, center of pressure (CoP) condition (explained subsequently), torque limits, etc., can be expressed as in Eq. 3

$$\displaystyle\begin{array}{rcl} \mathbf{J}_{c}(\ddot{\mathbf{q}})\, = \mathbf{b}(\mathbf{q},\dot{\mathbf{q}})\,,& &{}\end{array}$$

(2)

$$\displaystyle\begin{array}{rcl} \mathbf{A}[\ddot{\mathbf{q}}\ \ \ \boldsymbol{\tau }\ \ \ \mathbf{f}_{c}]^{T} \leq \mathbf{b}(\mathbf{q},\dot{\mathbf{q}})\,,& &{}\end{array}$$

(3)

The friction condition ensures that the robot feet do not slide on the ground, and the CoP condition corresponds to maintaining the resultant of the ground reaction force (GRF) within the perimeter of the support polygon (Sardain and Bessonnet 2004) so that toppling is prevented.

Some of the generalized coordinates of the robot, specifically those which describe the base link of the robot to the world frame, are not powered, as apparent from the joint torque vector representation $\boldsymbol{\varGamma }= [\mathbf{0}\ \ \boldsymbol{\tau }]^{T}$, in Eq. 1. In other words, the robot is called underactuated. In fact, all walking robots are underactuated, and it is one of the central characteristics that sets these robots apart from other robots. Underactuation plays a very important role in the dynamics, motion planning, and control of walking robots (Chevallereau et al. 2005).

Balance and Stability

Even after several decades of research, balance maintenance has remained one of the most important issues of walking robots and especially of humanoid robots. Although the basic dynamics of balance are currently understood (Sardain and Bessonnet 2004; Vukobratović and Juričić 1969), robust and general controllers that can deal with discrete and nonlevel foot support as well as large, unexpected, and unknown external disturbances such as from a moving support, a slip, and a trip have not yet emerged. In comparison with the elegance and versatility of human balance, present-day humanoid robots appear quite deficient.

Balance generally refers to the ability of a walking robot to maintain a sustained gait with a reasonably upright posture without falling (Kajita and Espiau 2008). Robot gait can be static or dynamic. A robot with a static gait would continue to stay upright even if its joints were suddenly frozen. Static gait and movement under static balance are safe but are slow and lacks elegance. A dynamic gait is fluid and natural looking as it harnesses and exploits the inertial characteristics of the physical robot. However, the robot must be in motion for it to sustain an upright stature. Suddenly locking the joints may cause a fall.

The location and the nature of the resultant GRF on the support polygon of the robot have been traditionally used to interpret the dynamic state of the robot’s movement. The point where the resultant GRF acts on the robot is called its zero moment point (ZMP), and it is equivalent to the CoP for planar support. Figure 11 explains the concept of CoP.

Walking Robots, Fig. 11

Definition of center of pressure (CoP), shown for one foot of a humanoid robot. The idea can be extended to any walking robot, and in a general setting, a single footprint is replaced by the support polygon which is the convex hull of all ground contact of the robot

As shown in Fig. 11, two types of interaction forces act on the foot at the foot/ground interface. They are the normal forces $\mathbf{f}_{ni}$, always directed upward (Fig. 11, left), and the frictional tangential forces $\mathbf{f}_{ti}$ (Fig. 11, middle). CoP, denoted by P, is the point where the resultant $\mathbf{R}_{n} =\sum \mathbf{f}_{ni}$ acts. With respect to a coordinate origin O, $\mathbf{OP} = \dfrac{\sum \mathbf{r}_{i}f_{ni}} {\sum f_{ni}}$, where $\mathbf{r}_{i}$ is the vector to the point of action of force $\mathbf{f}_{i}$ and f _ni is the magnitude of $\mathbf{f}_{ni}$.

Because of the unilaterality of the foot/ground constraint $\mathbf{f}_{ni} \geq 0$, which implies that P must lie within the support polygon. The resultant of the tangential forces may be represented at P by a force $\mathbf{R}_{t} =\sum \mathbf{f}_{ti}$ and a moment $\mathbf{M} =\sum \mathbf{r}_{i} \times \mathbf{f}_{ti}$ where $\mathbf{r}_{i}$ is the vector from P to the point of application of $\sum \mathbf{f}_{ti}$. A basic control objective for walking robots is to maintain the CoP within the perimeter of the support polygon.

Safety

Safety is a serious concern that is paramount to any application where robots are likely to coexist in interactive human environments. The power of mobility of walking robots adds to this concern.

Out of a number of possible situations where safety is an issue, one that involves a balance loss and fall is particularly worrisome for walking robots. All walking robots, and in fact all mobile robots, are subjected to this unique “failure” mode. A fall may be caused due to unexpected or excessive external forces, unusual or unknown slipperiness, and slope or profile of the ground, causing the robot to slip, trip, or topple. Fall can also result when the balance controller is partially or fully incapacitated due to an internal failure of the robot involving its sensor or actuator.

Fall can be costly in terms of the damage to the robot and also, depending on the shape and size of the robot, can result in external damage and injury to human.

For humanoid robots, fall is a particularly serious issue (Fujiwara et al. 2002). Humanoid robots, similar to humans, have a larger ratio of CoM height to support area size, which makes them more susceptible to fall, in case of a failure. At the same time, due to their higher CoM, a fall of such robots contains generally higher kinetic energy which is able to cause higher damage and injury.

Summary

Walking robots represent an important class of autonomous machines which can find application in the general area of service robotics. The power of mobility makes these robots uniquely capable of serving in niche need areas such as plant maintenance and security, disaster response, personal companion, and so on. Humanoid walking robots have attracted strong popular fascination, and this has fueled their rapid development. At present it appears that defense-related applications are the most likely to experience practical use of walking robots.

Walking robots possess interesting and complex kinematics and dynamics. Control of such machines, especially with regard to balancing, motion planning, and reactive behavior, is a rich research area that is challenging and demands special skill-sets.

Cross-References

• Disaster Response Robot

• Redundant Robots

• Robot Motion Control

• Robot Teleoperation

• Underactuated Robots

Recommended Reading

Out of the references listed below, Vukobratović and Juričić (1969) is the earliest paper dealing with bipedal robot balance, and it introduces the concept of ZMP. A very good recent overview of legged robots can be found in Kajita and Espiau (2008). Also of interest is the foundational paper on passive bipedal gait by McGeer (1990).