Inverted Pendulum Mechanism Research Articles

Adaptations to changing speed, load, and gradient in human walking: Cost of transport, optimal speed, and pendulum

It has been observed that the optimal speed (OPT) of human walking is independent of load on level surfaces because of the unaltered trajectory of the center of mass and consequent conservation of the pendular mechanism. However, the role of the inverted pendulum mechanism that combines speed, load, and gradient during walking remains unknown. In the present study, 10 subjects walked on a treadmill, with and without loading (25% of the body mass), at different speeds and slopes (0%, +7%, and +15%). The three-dimensional motion and VO2 were simultaneously registered. The mechanical external and internal work and the cost of transport (C) changed with the speed and gradient, but the load only affected C. OPT decreased with increasing gradient, and the pendular mechanics (R) was modified mainly as a result of changes in speed and gradient. OPT and R were independent of the load in these gradients. Remarkably, R increased with increasing speed and decreased (to 30%) with an increasing gradient; moreover, R was independent of load. Therefore, the energy-saving strategy by the pendular mechanism persists, although at a diminished level, in loaded walking on gradients and partially explains the OPT in this condition.

2A1-R14 車輪型倒立振子の凹凸路走行を実現するハイブリッドサスペンションの開発(車輪型/クローラ型移動ロボット(1))

2A1-R14 車輪型倒立振子の凹凸路走行を実現するハイブリッドサスペンションの開発(車輪型/クローラ型移動ロボット(1))

Postural Adjustments in Catching: On the Interplay Between Segment Stabilization and Equilibrium Control

The purpose of this study was to investigate postural adjustments in one-handed ball catching. Specifically, the functional role of anticipatory postural adjustments (APA) during the initial arm raising and subsequent postural adjustments (SPA) for equilibrium control and ball-hand impact were scrutinized. Full-body kinematics and kinetics allowed an analysis of the mechanical consequences of raising up the arm and preparing for ball-hand impact. APA for catching were suggested to be for segment stabilization. SPA had a functional role for equilibrium control by an inverted pendulum mechanism but were also involved in preparing for the impact of the ball on the hand, which was illustrated by an increased postural response at the end of the movement. These results were compared with raising up the arm in a well-studied reaction-time task, for which an additional counter rotation equilibrium mechanism was observed. Together, our findings demonstrate that postural adjustments should be investigated in relation to their specific functional task constraints, rather than generalizing the functional role of these postural adjustments over different tasks.

역진자 기구에 기반한 직립주행 가능 이동로봇용 구동 플랫폼 개발

In this research a moving platform for a mobile robot which can run with upright posture is proposed. It is able to stand with standing arms and run uprightly based on an inverted pendulum mechanism. Conventional mobile robots generally may equip 4 wheels or 3 wheels including a caster and have good statistic stability. They need a steering mechanism to choose which way to go since they have a square or rectangular configuration with multiple wheels. When a mobile robot meets a sharply perpendicular and narrow crossroad, it may need a special steering scheme such as going forward and backward repeatedly or it sometimes cannot even pass through the crossroad because of its size. The proposed moving platform for a mobile robot changes to a upright posture which has a small planar area and is able to pass through the crossroad. We propose a moving platform for a mobile robot with a inverted pendulum mechanism and standing arms which can make the mobile robot upright.

Kinematics and Center of Mass Mechanics During Terrestrial Locomotion in Northern Lapwings (Vanellus vanellus, Charadriiformes)

Avian bipedalism is best studied in derived walking/running specialists. Here, we use kinematics and center of mass (CoM) mechanical energy patterns to investigate gait transitions of lapwings-migratory birds that forage on the ground, and therefore may need a trade-off between the functional demands of terrestrial locomotion and long distance flights. The animals ran on a treadmill while high-speed X-ray videos were recorded within the sustainable speed range. Instantaneous CoM mechanics were computed from integrating kinematics and body segment properties. Lapwings exhibit similar locomotor characteristics to specialized walking/running birds, but have less distinct gaits. At slow speeds no clear separation between vaulting (i.e., walking) and bouncing (i.e., running) energy patterns exists. Mechanical energy recovery of non-bouncing gaits correlates poorly with speed and suggests inefficient use of the inverted pendulum mechanism. Speed ranges of gaits overlap considerably, especially those of grounded running, a gait with CoM mechanics indicative of running but without an aerial phase, and aerial phase running, with no preferential gait at most speeds. Compliant limb morphology and grounded running in birds can be regarded as an evolutionary constraint, but lapwings effectively make use of advantages offered by this gait for a great fraction of their speed range. Thus, effective usage of grounded running during terrestrial locomotion is suggested generally to be a part of striding avian bipedalism-even in species not specialized in walking/running locomotion.

Inefficient use of inverted pendulum mechanism during quadrupedal walking in the Japanese macaque

In animal walking, the gravitational potential and kinetic energy of the center of mass (COM) fluctuates out-of-phase to reduce the energetic cost of locomotion via an inverted pendulum mechanism, and, in canine quadrupedal walking, up to 70% of the mechanical energy can be recovered. However, the rate of energy recovery for quadrupedal walking in primates has been reported to be comparatively lower. The present study analyzed fluctuations in the potential and kinetic energy of the COM during quadrupedal walking in the Japanese macaque to clarify the mechanisms underlying this inefficient utilization of the inverted pendulum mechanism in primates. Monkeys walked on a wooden walkway at a self-selected speed, and ground reaction forces were measured, using a force platform, to calculate patterns of mechanical energy fluctuation and rates of energy recovery. Our results demonstrated that rates of energy recovery for quadrupedal walking in Japanese macaques were approximately 30-50%, much smaller than those reported for dogs. Comparisons of the patterns of mechanical energy fluctuation suggested that the potential and kinetic energies oscillated relatively more in-phase, and amplitudes did not attain near equality during quadrupedal walking in Japanese macaques, possibly because of greater weight support (reaction force) of the hindlimbs and more protracted forelimbs at touchdown in the Japanese macaque, two of the three commonly accepted locomotor characteristics distinguishing primates from non-primate mammals.

BigDog-Inspired Studies in the Locomotion of Goats and Dogs

Collision-based expenditure of mechanical energy and the compliance and geometry of the leg are fundamental, interrelated considerations in the mechanical design of legged runners. This article provides a basic context and rationale for experiments designed to inform each of these key areas in Boston Dynamic's BigDog robot. Although these principles have been investigated throughout the past few decades within different academic disciplines, BigDog required that they be considered together and in concert with an impressive set of control algorithms that are not discussed here. Although collision reduction is an important strategy for reducing mechanical cost of transport in the slowest and fastest quadrupedal gaits, walking and galloping, BigDog employed an intermediate-speed trotting gait without collision reduction. Trotting, instead, uses a spring-loaded inverted pendulum mechanism with potential for storage and return of elastic strain energy in appropriately compliant structures. Rather than tuning BigDog's built-in leg springs according to a spring-mass model-based virtual leg-spring constant , a much stiffer distal leg spring together with actuation of the adjacent joint provided good trotting dynamics and avoided functional limitations that might have been imposed by too much compliance in real-world terrain. Adjusting the directional compliance of the legs by adopting a knee-forward, elbow-back geometry led to more robust trotting dynamics by reducing perturbations about the pitch axis of the robot's center of mass (CoM). BigDog is the most successful large-scale, all-terrain trotting machine built to date and it continues to stimulate our understanding of legged locomotion in comparative biomechanics as well as in robotics.

Forward dynamic simulation of bipedal walking in the Japanese macaque: Investigation of causal relationships among limb kinematics, speed, and energetics of bipedal locomotion in a nonhuman primate

Japanese macaques that have been trained for monkey performances exhibit a remarkable ability to walk bipedally. In this study, we dynamically reconstructed bipedal walking of the Japanese macaque to investigate causal relationships among limb kinematics, speed, and energetics, with a view to understanding the mechanisms underlying the evolution of human bipedalism. We constructed a two-dimensional macaque musculoskeletal model consisting of nine rigid links and eight principal muscles. To generate locomotion, we used a trajectory-tracking control law, the reference trajectories of which were obtained experimentally. Using this framework, we evaluated the effects of changes in cycle duration and gait kinematics on locomotor efficiency. The energetic cost of locomotion was estimated based on the calculation of mechanical energy generated by muscles. Our results demonstrated that the mass-specific metabolic cost of transport decreased as speed increased in bipedal walking of the Japanese macaque. Furthermore, the cost of transport in bipedal walking was reduced when vertical displacement of the hip joint was virtually modified in the simulation to be more humanlike. Human vertical fluctuations in the body's center of mass actually contributed to energy savings via an inverted pendulum mechanism.

Mechanical Work and Metabolic Cost of Walking after Weight Loss in Obese Adolescents

This study was performed to investigate whether changes in biomechanical parameters of walking explain the reduction in net metabolic cost after weight loss in obese adolescents. Body composition and metabolic and mechanical energy costs of walking at 1.25 m·s(-1) were assessed in 16 obese adolescents before and after a weight loss. Center of mass (COM) and foot accelerations were measured using two inertial sensors and integrated twice to determine COM and foot velocities and displacements. Potential and kinetic energy fluctuations of the COM and the external mechanical work were calculated. Lateral leg swing was calculated from foot displacements. As expected, the decrease in net metabolic cost was greater, which would have been expected on the basis of the amount of weight loss. The smaller lateral leg swing after weight loss did not explain part of the decrease in net metabolic cost. The reduced body mass required less leg muscle work to raise and accelerate the COM as well as to support body weight. The decrease in body mass seems also associated with a lesser leg muscle work required to raise the COM because of smaller vertical motions. As a result of the inverted pendulum mechanism, the decrease in vertical motions (hence in potential energy fluctuations) was probably related to the decrease in mediolateral kinetic energy fluctuations. Moreover, the lesser amount of fat mass in the gynoid region seems related to the decrease in net metabolic cost of walking. The reduction in net metabolic cost of walking after weight loss in weight-reduced adolescents is associated with changes in the biomechanical parameters of walking.

Pound for pound: Working out how obesity influences the energetics of walking

Childhood and adult obesity are both serious health problems that are catalyzed by inadequate physical activity and the resulting chronic energy imbalance. For most people, walking consumes more metabolic energy than any other daily activity. Thus it is important to understand the energetic cost of

Low metabolic cost of locomotion in ornate box turtles,Terrapene ornata

Evolution has produced a wide range of body plans, but for a given body mass, the energetic cost of transport (COT) of terrestrial animals falls in a relatively narrow range. Previous research indicates that the COT depends on the proficiency of minimizing mechanical work performed, efficiency of performing that work, and cost of generating force to support weight. Turtles are unique in that their protective shell and shoulder-girdle articulation may eliminate the need for the ;muscular sling'. In addition, turtles have slower, more efficient muscles than other vertebrates. However, slow locomotion may raise the COT by confounding mechanical-energy conservation via the inverted-pendulum mechanism. Our goal was to determine the metabolic COT and efficiency of a terrestrial turtle species during locomotion. We studied 18 ornate box turtles, Terrapene ornata. Walking speed was extremely slow (0.07+/-0.005 m s(-1)). The average minimum COT was 8.0+/-0.70 J kg(-1) m(-1) attained at approximately 0.1 m s(-1). Ornate box turtles consume only half the energy predicted by the allometric relationship for all terrestrial animals (15.9+/-0.35 J kg(-1) m(-1)), and, thus, appear to be very economical walkers. When walking up a 24 deg. incline turtles moved significantly slower (0.04+/-0.004 m s(-1)), but performed the extra work required to walk uphill with very high efficiencies (>49%). It appears that the co-evolution of a protective shell, the associated shoulder morphology, and very slow, efficient muscles produce both economical level walking and efficient uphill walking.

The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective

We examine two prevailing, yet surprisingly contradictory, theories of human walking. The six determinants of gait are kinematic features of gait proposed to minimize the energetic cost of locomotion by reducing the vertical displacement of the body center of mass (COM). The inverted pendulum analogy proposes that it is beneficial for the stance leg to behave like a pendulum, prescribing a more circular arc, rather than a horizontal path, for the COM. Recent literature presents evidence against the six determinants theory, and a simple mathematical analysis shows that a flattened COM trajectory in fact increases muscle work and force requirements. A similar analysis shows that the inverted pendulum fares better, but paradoxically predicts no work or force requirements. The paradox may be resolved through the dynamic walking approach, which refers to periodic gaits produced almost entirely by the dynamics of the limbs alone. Demonstrations include passive dynamic walking machines that descend a gentle slope, and active dynamic walking robots that walk on level ground. Dynamic walking takes advantage of the inverted pendulum mechanism, but requires mechanical work to transition from one pendular stance leg to the next. We show how the step-to-step transition is an unavoidable energetic consequence of the inverted pendulum gait, and gives rise to predictions that are experimentally testable on humans and machines. The dynamic walking approach provides a new perspective, focusing on mechanical work rather than the kinematics or forces of gait. It is helpful for explaining human gait features in a constructive rather than interpretive manner.

The three-dimensional locomotor dynamics of African (Loxodonta africana) and Asian (Elephas maximus) elephants reveal a smooth gait transition at moderate speed.

We examined whether elephants shift to using bouncing (i.e. running) mechanics at any speed. To do this, we measured the three-dimensional centre of mass (CM) motions and torso rotations of African and Asian elephants using a novel multisensor method. Hundreds of continuous stride cycles were recorded in the field. African and Asian elephants moved very similarly. Near the mechanically and metabolically optimal speed (a Froude number (Fr) of 0.09), an inverted pendulum mechanism predominated. With increasing speed, the locomotor dynamics quickly but continuously became less like vaulting and more like bouncing. Our mechanical energy analysis of the CM suggests that at a surprisingly slow speed (approx. 2.2 m s(-1), Fr 0.25), the hindlimbs exhibited bouncing, not vaulting, mechanics during weight support. We infer that a gait transition happens at this relatively slow speed: elephants begin using their compliant hindlimbs like pogo sticks to some extent to drive the body, bouncing over their relatively stiff, vaulting forelimbs. Hence, they are not as rigid limbed as typically characterized for graviportal animals, and use regular walking as well as at least one form of running gait.

Patterns of mechanical energy change in tetrapod gait: pendula, springs and work

Kinematic and center of mass (CoM) mechanical variables used to define terrestrial gaits are compared for various tetrapod species. Kinematic variables (limb phase, duty factor) provide important timing information regarding the neural control and limb coordination of various gaits. Whereas, mechanical variables (potential and kinetic energy relative phase, %Recovery, %Congruity) provide insight into the underlying mechanisms that minimize muscle work and the metabolic cost of locomotion, and also influence neural control strategies. Two basic mechanisms identified by Cavagna et al. (1977. Am J Physiol 233:R243-R261) are used broadly by various bipedal and quadrupedal species. During walking, animals exchange CoM potential energy (PE) with kinetic energy (KE) via an inverted pendulum mechanism to reduce muscle work. During the stance period of running (including trotting, hopping and galloping) gaits, animals convert PE and KE into elastic strain energy in spring elements of the limbs and trunk and regain this energy later during limb support. The bouncing motion of the body on the support limb(s) is well represented by a simple mass-spring system. Limb spring compliance allows the storage and return of elastic energy to reduce muscle work. These two distinct patterns of CoM mechanical energy exchange are fairly well correlated with kinematic distinctions of limb movement patterns associated with gait change. However, in some cases such correlations can be misleading. When running (or trotting) at low speeds many animals lack an aerial period and have limb duty factors that exceed 0.5. Rather than interpreting this as a change of gait, the underlying mechanics of the body's CoM motion indicate no fundamental change in limb movement pattern or CoM dynamics has occurred. Nevertheless, the idealized, distinctive patterns of CoM energy fluctuation predicted by an inverted pendulum for walking and a bouncing mass spring for running are often not clear cut, especially for less cursorial species. When the kinematic and mechanical patterns of a broader diversity of quadrupeds and bipeds are compared, more complex patterns emerge, indicating that some animals may combine walking and running mechanics at intermediate speeds or at very large size. These models also ignore energy costs that are likely associated with the opposing action of limbs that have overlapping support times during walking. A recent model of terrestrial gait (Ruina et al., 2005. J Theor Biol, in press) that treats limb contact with the ground in terms of collisional energy loss indicates that considerable CoM energy can be conserved simply by matching the path of CoM motion perpendicular to limb ground force. This model, coupled with the earlier ones of pendular exchange during walking and mass-spring elastic energy savings during running, provides compelling argument for the view that the legged locomotion of quadrupeds and other terrestrial animals has generally evolved to minimize muscle work during steady level movement.

Adaptive stabilizing and tracking control for a nonlinear inverted-pendulum system via sliding-mode technique

Since the system behaviors of a dual-axis inverted-pendulum mechanism including actuator dynamics are highly nonlinear, it is difficult to design a suitable control system that realizes real-time stabilization and accurate tracking control at all times. In this paper, an adaptive sliding-mode control system is implemented to control a dual-axis inverted-pendulum mechanism that is driven by permanent magnet synchronous motors. First, the energy conservation principle is adopted to build a mathematical model of the motor-mechanism-coupled system. Moreover, an adaptive sliding-mode control system is developed for stabilizing and tracking control of the dual-axis inverted-pendulum system, where an adaptive algorithm is investigated to relax the requirement of the bound of lumped uncertainty in the traditional sliding-mode control. In addition, numerical simulation and experimental results show that the proposed control scheme provides high-performance dynamic characteristics and is robust with regard to parametric variations, various reference trajectories, and different initial states.

Stabilizing and tracking control of nonlinear dual-axis inverted-pendulum system using fuzzy neural network

Since the dynamic characteristics of a nonlinear inverted-pendulum mechanism are highly nonlinear, it is difficult to design a suitable control system that realizes real time stabilization and accurate tracking control at all time. In this study, a robust fuzzy-neural-network (FNN) control system is implemented to control a dual-axis inverted-pendulum mechanism that is driven by permanent magnet (PM) synchronous motors. The energy conservation principle is adopted to build a mathematical model of the motor-mechanism-coupled system. Moreover, a robust FNN control system is developed for stabilizing and tracking control of the dual-axis inverted-pendulum system. In this control system, a FNN controller is used to learn an equivalent control law as in the traditional sliding-mode control, and a robust controller is designed to ensure the near total sliding motion through the entire state trajectory without a reaching phase. The salient advantages of this FNN-based control scheme are as follows. 1) It does not require a perfect knowledge of system uncertainties so that this brings a high level of autonomy to the overall system and make the use of this control scheme very attractive for real time applications. 2) All adaptive learning algorithms in this control system are derived in the sense of Lyapunov stability analysis, so that system-tracking stability can be guaranteed in the closed-loop system. 3) Not only the weight vector in the rule-to-output layer are adjusted on line but also the mean and the standard deviation of Gaussian functions in the membership function layer. This training scheme will increase the learning capability of the FNN. 4) An adaptive bound estimation algorithm is investigated to relax the requirement for the bound of uncertain term including the minimum reconstructed error, higher-order term in Taylor series, and network parameters approximation error. The effectiveness of the proposed control strategy can be verified by numerical simulation and experimental results.

Energy expenditure of bipedal walking is higher than that of quadrupedal walking in Japanese macaques

The authors previously compared energetic costs of bipedal and quadrupedal walking in bipedally trained macaques used for traditional Japanese monkey performances (Nakatsukasa et al. 2004 Am. J. Phys. Anthropol. 124:248-256). These macaques used inverted pendulum mechanics during bipedal walking, which resulted in an efficient exchange of potential and kinetic energy. Nonetheless, energy expenditure during bipedal walking was significantly higher than that of quadrupedal walking. In Nakatsukasa et al. (2004 Am. J. Phys. Anthropol. 124:248-256), locomotor costs were measured before subjects reached a steady state due to technical limitations. The present investigation reports sequential changes of energy consumption during 15 min of walking in two trained macaques, using carbon dioxide production as a proxy of energy consumption, as in Nakatsukasa et al. (2004 Am. J. Phys. Anthropol. 124:248-256). Although a limited number of sessions were conducted, carbon dioxide production was consistently greater during bipedal walking, with the exception of some irregularity during the first minute. Carbon dioxide production gradually decreased after 1 min, and both subjects reached a steady state within 10 min. Energy expenditure during bipedalism relative to quadrupedalism differed between the two subjects. It was considerably higher (140% of the quadrupedal walking cost) in one subject who walked with more bent-knee, bent-hip gaits. This high cost strongly suggests that ordinary macaques, who adopt further bent-knee, bent-hip gaits, consume a far greater magnitude of energy during bipedal walking.

Multi-Input Fuzzy control of an inverted pendulum using an armature controlled DC motor

This paper presents a design methodology to stabilize a class of multi-variant nonlinear system after a high disturbance occurs. It investigates application of Takagi-Sugeno type fuzzy controller (T-S-FC) to an inverted pendulum mechanism, actuated by an armature-controlled DC electrical motor.Fuzzy controllers use heuristic information in developing design methodologies for control of non-linear dynamic systems. This approach eliminates the need for comprehensive knowledge and mathematical modeling of the system, and in cases of more complex systems, approximation and simplifications in order to achieve feasible mathematical model is not required.The paper presents the stages of development of the Fuzzy Controller for an inverted pendulum by developing a two-input, Mamdani type system. It evaluates the performance of the system. Then a four-input T-S-FC type is developed. The research compares performances of each controller and presents the result of tests. A model for a DC motor is developed in this study, in order to measure the effect of time delays and response time caused by inherent properties of the physical system. The final part will demonstrate the complete operational system with the DC electrical motor included in the test system.

Why not walk faster?

Bipedal walking following inverted pendulum mechanics is constrained by two requirements: sufficient kinetic energy for the vault over midstance and sufficient gravity to provide the centripetal acceleration required for the arc of the body about the stance foot. While the acceleration condition identifies a maximum walking speed at a Froude number of 1, empirical observation indicates favoured walk-run transition speeds at a Froude number around 0.5 for birds, humans and humans under manipulated gravity conditions. In this study, I demonstrate that the risk of 'take-off' is greatest at the extremes of stance. This is because before and after kinetic energy is converted to potential, velocities (and so required centripetal accelerations) are highest, while concurrently the component of gravity acting in line with the leg is least. Limitations to the range of walking velocity and stride angle are explored. At walking speeds approaching a Froude number of 1, take-off is only avoidable with very small steps. With realistic limitations on swing-leg frequency, a novel explanation for the walk-run transition at a Froude number of 0.5 is shown.

TRUDGING TORTOISES

When Darwin made his historic HMS Beagle voyage, one animal in particular caught his eye: the giant Galápagos tortoise, plodding along at a leisurely 0.16 metres per second. Intrigued by the hefty reptile's painfully slow pace, Peter Zani and colleagues at the University of Colorado,Boulder, decided to put giant tortoises through their paces(p. 1489).Zani wondered whether tortoises, just like many other animals, use a mechanism known as the inverted pendulum to conserve mechanical energy as they amble along. He explains that as you walk, the potential energy that is associated with the height of your centre of mass changes into kinetic energy. When your foot touches the ground, lifting your centre of mass, this kinetic energy is converted back to potential energy. `Throughout this energy exchange, your centre of mass rises and falls in the shape of an inverted pendulum,' Zani says. It's an efficient mechanism to recover energy, but do giant Galápagos tortoises use it?According to Zani, `two conditions have to be met to show that the inverted pendulum mechanism is at work.' First, kinetic and potential energy should be out of phase – as kinetic energy rises, potential energy falls. Second,fluctuations in kinetic and potential energy must be of equal magnitude and shape. Since kinetic energy is the energy of motion, and giant tortoises are so slow, they are likely to have very small kinetic energy fluctuations. Teaming up with Rodger Kram, Zani calculated that if tortoises use the inverted pendulum mechanism, their modest kinetic energy should raise their centre of mass vertically by only 0.5 mm. But tortoises sway as they walk, so Zani and Kram suspected that they don't use the inverted pendulum mechanism.To test this, they needed to analyse the mechanical energy patterns of travelling tortoises. Zani widened and strengthened a traditional force plate walkway to cope with the bulk of the giant creatures. If he could convince tortoises to walk across it, he'd be able to convert its force measurements into mechanical energy values. Jinger Gottschall joined Zani and Kram as they loaded the modified walkway into a trailer and drove to the Oklahoma City Zoo. Once there, they were faced with the challenge of luring five giant Galápagos tortoises up a ramp onto the walkway. Zani soon found that`you can't force a 200 kg animal to do what you want!' But tempting the creatures with juicy apples and carrots seemed to do the trick, and the team videotaped them as they lumbered across the walkway to get their treat.Analysing the force plate measurements and video footage with Gottschall,Zani could see that the tortoises didn't meet the two conditions. Their kinetic and potential energies fluctuated randomly – sometimes they were in phase, sometimes they were out of phase. `There was certainly no systematic exchange of energy,' he says.They also saw that a giant tortoise's centre of mass rises about 1.5 cm as it walks, much more than the 0.5 mm predicted if they use the energy-conserving mechanism. As the team had suspected, giant Galápagos tortoises do not use the inverted pendulum mechanism. Yet despite their inefficient pace, Zani notes that giant tortoises don't have to work harder than other animals to travel the same distance.