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1.  Swing-Leg Trajectory of Running Guinea Fowl Suggests Task-Level Priority of Force Regulation Rather than Disturbance Rejection 
PLoS ONE  2014;9(6):e100399.
To achieve robust and stable legged locomotion in uneven terrain, animals must effectively coordinate limb swing and stance phases, which involve distinct yet coupled dynamics. Recent theoretical studies have highlighted the critical influence of swing-leg trajectory on stability, disturbance rejection, leg loading and economy of walking and running. Yet, simulations suggest that not all these factors can be simultaneously optimized. A potential trade-off arises between the optimal swing-leg trajectory for disturbance rejection (to maintain steady gait) versus regulation of leg loading (for injury avoidance and economy). Here we investigate how running guinea fowl manage this potential trade-off by comparing experimental data to predictions of hypothesis-based simulations of running over a terrain drop perturbation. We use a simple model to predict swing-leg trajectory and running dynamics. In simulations, we generate optimized swing-leg trajectories based upon specific hypotheses for task-level control priorities. We optimized swing trajectories to achieve i) constant peak force, ii) constant axial impulse, or iii) perfect disturbance rejection (steady gait) in the stance following a terrain drop. We compare simulation predictions to experimental data on guinea fowl running over a visible step down. Swing and stance dynamics of running guinea fowl closely match simulations optimized to regulate leg loading (priorities i and ii), and do not match the simulations optimized for disturbance rejection (priority iii). The simulations reinforce previous findings that swing-leg trajectory targeting disturbance rejection demands large increases in stance leg force following a terrain drop. Guinea fowl negotiate a downward step using unsteady dynamics with forward acceleration, and recover to steady gait in subsequent steps. Our results suggest that guinea fowl use swing-leg trajectory consistent with priority for load regulation, and not for steadiness of gait. Swing-leg trajectory optimized for load regulation may facilitate economy and injury avoidance in uneven terrain.
doi:10.1371/journal.pone.0100399
PMCID: PMC4076256  PMID: 24979750
2.  Don't break a leg: running birds from quail to ostrich prioritise leg safety and economy on uneven terrain 
The Journal of Experimental Biology  2014;217(21):3786-3796.
Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics.
doi:10.1242/jeb.102640
PMCID: PMC4213177  PMID: 25355848
Bipedal running; Gait stability; Ground birds; Injury avoidance; Trajectory optimisation
3.  Running stability is enhanced by a proximo-distal gradient in joint neuromechanical control 
The Journal of experimental biology  2007;210(Pt 3):383-394.
Summary
We currently know little about how animals achieve dynamic stability when running over uneven and unpredictable terrain, often characteristic of their natural environment. Here we investigate how limb and joint mechanics of an avian biped, the helmeted guinea fowl Numida meleagris, respond to an unexpected drop in terrain during running. In particular, we address how joint mechanics are coordinated to achieve whole limb dynamics. Based on muscle–tendon architecture and previous studies of steady and incline locomotion, we hypothesize a proximo-distal gradient in joint neuromechanical control. In this motor control strategy, (1) proximal muscles at the hip and knee joints are controlled primarily in a feedforward manner and exhibit load-insensitive mechanical performance, and (2) distal muscles at the ankle and tarsometatarso-phalangeal (TMP) joints are highly load-sensitive, due to intrinsic mechanical effects and rapid, higher gain proprioceptive feedback. Limb kinematics and kinetics during the unexpected perturbation reveal that limb retraction, controlled largely by the hip, remains similar to level running throughout the perturbed step, despite altered limb loading. Individual joints produce or absorb energy during both level and perturbed running steps, such that the net limb work depends on the balance of energy among the joints. The hip maintains the same mechanical role regardless of limb loading, whereas the ankle and TMP switch between spring-like or damping function depending on limb posture at ground contact. Initial knee angle sets limb posture and alters the balance of work among the joints, although the knee contributes little work itself. This distribution of joint function results in posture-dependent changes in work performance of the limb, which allow guinea fowl to rapidly produce or absorb energy in response to the perturbation. The results support the hypothesis that a proximo-distal gradient exists in limb neuromuscular performance and motor control. This control strategy allows limb cycling to remain constant, whereas limb posture, loading and energy performance are interdependent. We propose that this control strategy provides simple, rapid mechanisms for managing energy and controlling velocity when running over rough terrain.
doi:10.1242/jeb.02668
PMCID: PMC2413410  PMID: 17234607
running; locomotion; biomechanics; motor control; joint work; joint moment; inverse dynamics
4.  Leg muscles that mediate stability: mechanics and control of two distal extensor muscles during obstacle negotiation in the guinea fowl 
Here, we used an obstacle treadmill experiment to investigate the neuromuscular control of locomotion in uneven terrain. We measured in vivo function of two distal muscles of the guinea fowl, lateral gastrocnemius (LG) and digital flexor-IV (DF), during level running, and two uneven terrains, with 5 and 7 cm obstacles. Uneven terrain required one step onto an obstacle every four to five strides. We compared both perturbed and unperturbed strides in uneven terrain to level terrain. When the bird stepped onto an obstacle, the leg became crouched, both muscles acted at longer lengths and produced greater work, and body height increased. Muscle activation increased on obstacle strides in the LG, but not the DF, suggesting a greater reflex contribution to LG. In unperturbed strides in uneven terrain, swing pre-activation of DF increased by 5 per cent compared with level terrain, suggesting feed-forward tuning of leg impedance. Across conditions, the neuromechanical factors in work output differed between the two muscles, probably due to differences in muscle–tendon architecture. LG work depended primarily on fascicle length, whereas DF work depended on both length and velocity during loading. These distal muscles appear to play a critical role in stability by rapidly sensing and responding to altered leg–ground interaction.
doi:10.1098/rstb.2010.0338
PMCID: PMC3130446  PMID: 21502128
locomotion; biomechanics; motor control
5.  Human hopping on damped surfaces: strategies for adjusting leg mechanics. 
Fast-moving legged animals bounce along the ground with spring-like legs and agilely traverse variable terrain. Previous research has shown that hopping and running humans maintain the same bouncing movement of the body's centre of mass on a range of elastic surfaces by adjusting their spring-like legs to exactly offset changes in surface stiffness. This study investigated human hopping on damped surfaces that dissipated up to 72% of the hopper's mechanical energy. On these surfaces, the legs did not act like pure springs. Leg muscles performed up to 24-fold more net work to replace the energy lost by the damped surface. However, considering the leg and surface together, the combination appeared to behave like a constant stiffness spring on all damped surfaces. By conserving the mechanics of the leg-surface combination regardless of surface damping, hoppers also conserved centre-of-mass motions. Thus, the normal bouncing movements of the centre of mass in hopping are not always a direct result of spring-like leg behaviour. Conserving the trajectory of the centre of mass by maintaining spring-like mechanics of the leg-surface combination may be an important control strategy for fast-legged locomotion on variable terrain.
doi:10.1098/rspb.2003.2435
PMCID: PMC1691428  PMID: 12965003
6.  Effects of a Foot Placement Constraint on Use of Motor Equivalence during Human Hopping 
PLoS ONE  2013;8(7):e69429.
Humans can robustly locomote over complex terrains even while simultaneously attending to other tasks such as accurate foot placement on the ground. We investigated whether subjects would exploit motor redundancy across the joints of the leg to stabilize overall limb kinematics when presented with a hopping task that constrained foot placement position. Subjects hopped in place on one leg (2.2 Hz) while having to place their foot into one of three target sizes upon landing (0.250, 0.063, 0.010 m2). As takeoff and landing angles are critical to this task performance, we hypothesized smaller target sizes would increase the need to stabilize (i.e., make more consistent) the leg orientation through motor equivalent combinations of segment angles. As it was not critical to the targeting task, we hypothesized no changes for leg length stabilization across target size. With smaller target sizes, we saw total segment angle variance increase due to greater signal-dependent noise associated with an increased activation of leg extensor muscles (medial and lateral gastrocnemius, vastus medialis, vastus lateralis and rectus femoris). At smaller target sizes, more segment angle variance was aligned to kinematic deviations with the goal of maintaining leg orientation trajectory. We also observed a decrease in the variance structure for stabilizing leg length at the smallest target conditions. This trade-off effect is explained by the nearly orthogonal relationship between the two goal-equivalent manifolds for leg length vs. leg orientation stabilization. Our results suggest humans increasingly rely on kinematic redundancy in their legs to achieve robust, consistent locomotion when faced with novel conditions that constrain performance requirements. These principles may generalize to other human locomotor gaits and provide important insights into the control of the legs during human walking and running.
doi:10.1371/journal.pone.0069429
PMCID: PMC3728346  PMID: 23936013
7.  Positive force feedback in bouncing gaits? 
During bouncing gaits (running, hopping, trotting), passive compliant structures (e.g. tendons, ligaments) store and release part of the stride energy. Here, active muscles must provide the required force to withstand the developing tendon strain and to compensate for the inevitable energy losses. This requires an appropriate control of muscle activation. In this study, for hopping, the potential involvement of afferent information from muscle receptors (muscle spindles, Golgi tendon organs) is investigated using a two-segment leg model with one extensor muscle. It is found that: (i) positive feedbacks of muscle-fibre length and muscle force can result in periodic bouncing; (ii) positive force feedback (F+) stabilizes bouncing patterns within a large range of stride energies (maximum hopping height of 16.3 cm, almost twofold higher than the length feedback); and (iii) when employing this reflex scheme, for moderate hopping heights (up to 8.8 cm), an overall elastic leg behaviour is predicted (hopping frequency of 1.4-3 Hz, leg stiffness of 9-27 kN m(-1)). Furthermore, F+ could stabilize running. It is suggested that, during the stance phase of bouncing tasks, the reflex-generated motor control based on feedbacks might be an efficient and reliable alternative to central motor commands.
doi:10.1098/rspb.2003.2454
PMCID: PMC1691493  PMID: 14561282
8.  Kinematic primitives for walking and trotting gaits of a quadruped robot with compliant legs 
In this work we research the role of body dynamics in the complexity of kinematic patterns in a quadruped robot with compliant legs. Two gait patterns, lateral sequence walk and trot, along with leg length control patterns of different complexity were implemented in a modular, feed-forward locomotion controller. The controller was tested on a small, quadruped robot with compliant, segmented leg design, and led to self-stable and self-stabilizing robot locomotion. In-air stepping and on-ground locomotion leg kinematics were recorded, and the number and shapes of motion primitives accounting for 95% of the variance of kinematic leg data were extracted. This revealed that kinematic patterns resulting from feed-forward control had a lower complexity (in-air stepping, 2–3 primitives) than kinematic patterns from on-ground locomotion (νm4 primitives), although both experiments applied identical motor patterns. The complexity of on-ground kinematic patterns had increased, through ground contact and mechanical entrainment. The complexity of observed kinematic on-ground data matches those reported from level-ground locomotion data of legged animals. Results indicate that a very low complexity of modular, rhythmic, feed-forward motor control is sufficient for level-ground locomotion in combination with passive compliant legged hardware.
doi:10.3389/fncom.2014.00027
PMCID: PMC3945928  PMID: 24639645
motion primitives; locomotion patterns; central pattern generator; quadruped robot; passive leg compliance; entrainment; principal component analysis; walk and trot
9.  Task-Level Strategies for Human Sagittal-Plane Running Maneuvers Are Consistent with Robotic Control Policies 
PLoS ONE  2012;7(12):e51888.
The strategies that humans use to control unsteady locomotion are not well understood. A “spring-mass” template comprised of a point mass bouncing on a sprung leg can approximate both center of mass movements and ground reaction forces during running in humans and other animals. Legged robots that operate as bouncing, “spring-mass” systems can maintain stable motion using relatively simple, distributed feedback rules. We tested whether the changes to sagittal-plane movements during five running tasks involving active changes to running height, speed, and orientation were consistent with the rules used by bouncing robots to maintain stability. Changes to running height were associated with changes to leg force but not stance duration. To change speed, humans primarily used a “pogo stick” strategy, where speed changes were associated with adjustments to fore-aft foot placement, and not a “unicycle” strategy involving systematic changes to stance leg hip moment. However, hip moments were related to changes to body orientation and angular speed. Hip moments could be described with first order proportional-derivative relationship to trunk pitch. Overall, the task-level strategies used for body control in humans were consistent with the strategies employed by bouncing robots. Identification of these behavioral strategies could lead to a better understanding of the sensorimotor mechanisms that allow for effective unsteady locomotion.
doi:10.1371/journal.pone.0051888
PMCID: PMC3527458  PMID: 23284804
10.  Directionally compliant legs influence the intrinsic pitch behaviour of a trotting quadruped 
Limb design is well conserved among quadrupeds, notably, the knees point forward (i.e. cranial inclination of femora) and the elbows point back (i.e. caudal inclination of humeri). This study was undertaken to examine the effects of joint orientation on individual leg forces and centre of mass dynamics. Steady-speed trotting was simulated in two quadrupedal models. Model I had the knee and elbow orientation of a quadruped and model II had a reversed leg configuration in which knees point back and elbows point forward. The model's legs showed directional compliance determined by the orientation of the knee/elbow. In both models, forward pointing knees/elbows produced a propulsive force bias, while rearward pointing knees/elbows produced a braking force bias. Hence, model I showed the same pattern of hind-leg propulsion and fore-leg braking observed in trotting animals. Simulations revealed minimal pitch oscillations during steady-speed trotting of model I, but substantially greater and more irregular pitch oscillations of model II. The reduced pitch oscillation of model I was a result of fore-leg and hind-leg forces that reduced pitching moments during early and late stance, respectively. This passive mechanism for reducing pitch oscillations was an emergent property of directionally compliant legs with the fore–hind configuration of model I. Such intrinsic stability resulting from mechanical design can simplify control tasks and lead to more robust running machines.
doi:10.1098/rspb.2004.3014
PMCID: PMC1564074  PMID: 15817430
locomotion; simulation; running; ground reaction force; pitch
11.  Fifteen observations on the structure of energy-minimizing gaits in many simple biped models 
A popular hypothesis regarding legged locomotion is that humans and other large animals walk and run in a manner that minimizes the metabolic energy expenditure for locomotion. Here, using numerical optimization and supporting analytical arguments, I obtain the energy-minimizing gaits of many different simple biped models. I consider bipeds with point-mass bodies and massless legs, with or without a knee, with or without a springy tendon in series with the leg muscle and minimizing one of many different ‘metabolic cost’ models—correlated with muscle work, muscle force raised to some power, the Minetti–Alexander quasi-steady approximation to empirical muscle metabolic rate (from heat and ATPase activity), a new cost function called the ‘generalized work cost’ Cg having some positivity and convexity properties (and includes the Minetti–Alexander cost and the work cost as special cases), and generalizations thereof. For many of these models, walking-like gaits are optimal at low speeds and running-like gaits at higher speeds, so a gait transition is optimal. Minimizing the generalized work cost Cg appears mostly indistinguishable from minimizing muscle work for all the models. Inverted pendulum walking and impulsive running gaits minimize the work cost, generalized work costs Cg and a few other costs for the springless bipeds; in particular, a knee-torque-squared cost, appropriate as a simplified model for electric motor power for a kneed robot biped. Many optimal gaits had symmetry properties; for instance, the left stance phase was identical to the right stance phases. Muscle force–velocity relations and legs with masses have predictable qualitative effects, if any, on the optima. For bipeds with compliant tendons, the muscle work-minimizing strategies have close to zero muscle work (isometric muscles), with the springs performing all the leg work. These zero work gaits also minimize the generalized work costs Cg with substantial additive force or force rate costs, indicating that a running animal's metabolic cost could be dominated by the cost of producing isometric force, even though performing muscle work is usually expensive. I also catalogue the many differences between the optimal gaits of the various models. These differences contain information that might help us develop models that better predict locomotion data. In particular, for some biologically plausible cost functions, the presence or absence of springs in series with muscles has a large effect on both the coordination strategy and the absolute cost; the absence of springs results in more impulsive (collisional) optimal gaits and the presence of springs leads to more compliant optimal gaits. Most results are obtained for specific speed and stride length combinations close to preferred human behaviour, but limited numerical experiments show that some qualitative results extend to other speed-stride length combinations as well.
doi:10.1098/rsif.2009.0544
PMCID: PMC3024815  PMID: 20542957
legged locomotion; walking and running; optimization and optimal control; minimize energy; gaits; metabolic cost
12.  People Bouncing on Trampolines: Dramatic Energy Transfer, a Table-Top Demonstration, Complex Dynamics and a Zero Sum Game 
PLoS ONE  2013;8(11):e78645.
Jumping on trampolines is a popular backyard recreation. In some trampoline games (e.g., “seat drop war”), when two people land on the trampoline with only a small time-lag, one person bounces much higher than the other, as if energy has been transferred from one to the other. First, we illustrate this energy-transfer in a table-top demonstration, consisting of two balls dropped onto a mini-trampoline, landing almost simultaneously, sometimes resulting in one ball bouncing much higher than the other. Next, using a simple mathematical model of two masses bouncing passively on a massless trampoline with no dissipation, we show that with specific landing conditions, it is possible to transfer all the kinetic energy of one mass to the other through the trampoline – in a single bounce. For human-like parameters, starting with equal energy, the energy transfer is maximal when one person lands approximately when the other is at the bottom of her bounce. The energy transfer persists even for very stiff surfaces. The energy-conservative mathematical model exhibits complex non-periodic long-term motions. To complement this passive bouncing model, we also performed a game-theoretic analysis, appropriate when both players are acting strategically to steal the other player's energy. We consider a zero-sum game in which each player's goal is to gain the other player's kinetic energy during a single bounce, by extending her leg during flight. For high initial energy and a symmetric situation, the best strategy for both subjects (minimax strategy and Nash equilibrium) is to use the shortest available leg length and not extend their legs. On the other hand, an asymmetry in initial heights allows the player with more energy to gain even more energy in the next bounce. Thus synchronous bouncing unstable is unstable both for passive bouncing and when leg lengths are controlled as in game-theoretic equilibria.
doi:10.1371/journal.pone.0078645
PMCID: PMC3827250  PMID: 24236029
13.  Stability and Responsiveness in a Self-Organized Living Architecture 
PLoS Computational Biology  2013;9(3):e1002984.
Robustness and adaptability are central to the functioning of biological systems, from gene networks to animal societies. Yet the mechanisms by which living organisms achieve both stability to perturbations and sensitivity to input are poorly understood. Here, we present an integrated study of a living architecture in which army ants interconnect their bodies to span gaps. We demonstrate that these self-assembled bridges are a highly effective means of maintaining traffic flow over unpredictable terrain. The individual-level rules responsible depend only on locally-estimated traffic intensity and the number of neighbours to which ants are attached within the structure. We employ a parameterized computational model to reveal that bridges are tuned to be maximally stable in the face of regular, periodic fluctuations in traffic. However analysis of the model also suggests that interactions among ants give rise to feedback processes that result in bridges being highly responsive to sudden interruptions in traffic. Subsequent field experiments confirm this prediction and thus the dual nature of stability and flexibility in living bridges. Our study demonstrates the importance of robust and adaptive modular architecture to efficient traffic organisation and reveals general principles regarding the regulation of form in biological self-assemblies.
Author Summary
While migrating, the nomadic army ant Eciton burchellii forms long trails of workers that can extend over hundreds of meters in the rain forest. To facilitate the movement of sometimes millions of individuals on uneven and unpredictable terrains, part of the ant workers link together their legs and bodies to form temporary bridges over gaps along the trails. In this work we showed that these bridges were formed readily when the flow of ants hit an unspanned gap and were dismantled very quickly after traffic has ceased on the trail. However, we also observed that the bridges were formed and remained stable under a large spectrum of the traffic intensities on the trail. Using field experiments and computer simulations we discovered the construction rules used by the ants to create these living structures that are capable of enduring variations of the traffic while remaining highly responsive to its interruption. These results offer important insights about the mechanisms that regulate biological self-assemblies and they have potential applications in swarm robotics and swarm intelligence.
doi:10.1371/journal.pcbi.1002984
PMCID: PMC3610604  PMID: 23555219
14.  Human Leg Model Predicts Ankle Muscle-Tendon Morphology, State, Roles and Energetics in Walking 
PLoS Computational Biology  2011;7(3):e1001107.
A common feature in biological neuromuscular systems is the redundancy in joint actuation. Understanding how these redundancies are resolved in typical joint movements has been a long-standing problem in biomechanics, neuroscience and prosthetics. Many empirical studies have uncovered neural, mechanical and energetic aspects of how humans resolve these degrees of freedom to actuate leg joints for common tasks like walking. However, a unifying theoretical framework that explains the many independent empirical observations and predicts individual muscle and tendon contributions to joint actuation is yet to be established. Here we develop a computational framework to address how the ankle joint actuation problem is resolved by the neuromuscular system in walking. Our framework is founded upon the proposal that a consideration of both neural control and leg muscle-tendon morphology is critical to obtain predictive, mechanistic insight into individual muscle and tendon contributions to joint actuation. We examine kinetic, kinematic and electromyographic data from healthy walking subjects to find that human leg muscle-tendon morphology and neural activations enable a metabolically optimal realization of biological ankle mechanics in walking. This optimal realization (a) corresponds to independent empirical observations of operation and performance of the soleus and gastrocnemius muscles, (b) gives rise to an efficient load-sharing amongst ankle muscle-tendon units and (c) causes soleus and gastrocnemius muscle fibers to take on distinct mechanical roles of force generation and power production at the end of stance phase in walking. The framework outlined here suggests that the dynamical interplay between leg structure and neural control may be key to the high walking economy of humans, and has implications as a means to obtain insight into empirically inaccessible features of individual muscle and tendons in biomechanical tasks.
Author Summary
Biological neuromuscular systems are generally able to perform a specified movement task in several ways – as they have significantly more degrees of freedom than mechanical constraints. Understanding how humans resolve these redundancies to drive individual muscles and tendons in typical joint movements is of interest in the fields of biomechanics, neuroscience and prosthetics. Many experimental studies have uncovered neural, mechanical and energetic features of individual muscle and tendon function in common tasks like walking and running. However, a unifying theoretical framework that explains the many independent empirical observations is yet to be established. In this work, we show that leg muscle-tendon morphology and neural co-ordination, together, enable efficient ankle movements in walking. This finding provides quantitative insight into the operation and performance of posterior-leg muscles and tendons in walking, and motivates the idea that different muscle-tendon units take on different mechanical roles to best actuate the ankle in gait. Results reported have implications both for better understanding neuromuscular co-ordination in gait, and for the design of lower limb prosthetic and orthotic technologies.
doi:10.1371/journal.pcbi.1001107
PMCID: PMC3060164  PMID: 21445231
15.  Running in the real world: adjusting leg stiffness for different surfaces. 
A running animal coordinates the actions of many muscles, tendons, and ligaments in its leg so that the overall leg behaves like a single mechanical spring during ground contact. Experimental observations have revealed that an animal's leg stiffness is independent of both speed and gravity level, suggesting that it is dictated by inherent musculoskeletal properties. However, if leg stiffness was invariant, the biomechanics of running (e.g. peak ground reaction force and ground contact time) would change when an animal encountered different surfaces in the natural world. We found that human runners adjust their leg stiffness to accommodate changes in surface stiffness, allowing them to maintain similar running mechanics on different surfaces. These results provide important insight into mechanics and control of animal locomotion and suggest that incorporating an adjustable leg stiffness in the design of hopping and running robots is important if they are to match the agility and speed of animals on varied terrain.
PMCID: PMC1689165  PMID: 9675909
16.  Applying the cost of generating force hypothesis to uphill running 
PeerJ  2014;2:e482.
Historically, several different approaches have been applied to explain the metabolic cost of uphill human running. Most of these approaches result in unrealistically high values for the efficiency of performing vertical work during running uphill, or are only valid for running up steep inclines. The purpose of this study was to reexamine the metabolic cost of uphill running, based upon our understanding of level running energetics and ground reaction forces during uphill running. In contrast to the vertical efficiency approach, we propose that during incline running at a certain velocity, the forces (and hence metabolic energy) required for braking and propelling the body mass parallel to the running surface are less than during level running. Based on this idea, we propose that the metabolic rate during uphill running can be predicted by a model, which posits that (1) the metabolic cost of perpendicular bouncing remains the same as during level running, (2) the metabolic cost of running parallel to the running surface decreases with incline, (3) the delta efficiency of producing mechanical power to lift the COM vertically is constant, independent of incline and running velocity, and (4) the costs of leg and arm swing do not change with incline. To test this approach, we collected ground reaction force (GRF) data for eight runners who ran thirty 30-second trials (velocity: 2.0–3.0 m/s; incline: 0–9°). We also measured the metabolic rates of eight different runners for 17, 7-minute trials (velocity: 2.0–3.0 m/s; incline: 0–8°). During uphill running, parallel braking GRF approached zero for the 9° incline trials. Thus, we modeled the metabolic cost of parallel running as exponentially decreasing with incline. With that assumption, best-fit parameters for the metabolic rate data indicate that the efficiency of producing mechanical power to lift the center of mass vertically was independent of incline and running velocity, with a value of ∼29%. The metabolic cost of uphill running is not simply equal to the sum of the cost of level running and the cost of performing work to lift the body mass against gravity. Rather, it reflects a constant cost of perpendicular bouncing, decreased costs of parallel braking and propulsion and of course the cost of lifting body mass against gravity.
doi:10.7717/peerj.482
PMCID: PMC4106190  PMID: 25083347
Incline; Locomotion; Efficiency; Metabolic cost; Oxygen consumption; Biomechanics
17.  Preliminary Design of a Terrain Recognition System 
This paper aims to design a wearable terrain recognition system, which might assist the control of powered artificial prosthetic legs. A laser distance sensor and inertial measurement unit (IMU) sensors were mounted on human body. These sensors were used to identify the movement state of the user, reconstruct the geometry of the terrain in front of the user while walking, and recognize the type of terrain before the user stepped on it. Different sensor configurations were investigated and compared. The designed system was evaluated on one healthy human subject when walking on an obstacle course in the laboratory environment. The results showed that the reconstructed terrain height demonstrated clearer pattern difference among studied terrains when the laser was placed on the waist than that when the laser was mounted on the shank. The designed system with the laser on the waist accurately recognized 157 out of 160 tested terrain transitions, 300ms–2870ms before the user switched the negotiated terrains. These promising results demonstrated the potential application of the designed terrain recognition system to further improve the control of powered artificial legs.
doi:10.1109/IEMBS.2011.6091391
PMCID: PMC3718465  PMID: 22255571
18.  Stance controlled knee flexion improves stimulation driven walking after spinal cord injury 
Background
Functional neuromuscular stimulation (FNS) restores walking function after paralysis from spinal cord injury via electrical activation of muscles in a coordinated fashion. Combining FNS with a controllable orthosis to create a hybrid neuroprosthesis (HNP) has the potential to extend walking distance and time by mechanically locking the knee joint during stance to allow knee extensor muscle to rest with stimulation turned off. Recent efforts have focused on creating advanced HNPs which couple joint motion (e.g., hip and knee or knee and ankle) to improve joint coordination during swing phase while maintaining a stiff-leg during stance phase.
Methods
The goal of this study was to investigate the effects of incorporating stance controlled knee flexion during loading response and pre-swing phases on restored gait. Knee control in the HNP was achieved by a specially designed variable impedance knee mechanism (VIKM). One subject with a T7 level spinal cord injury was enrolled and served as his own control in examining two techniques to restore level over-ground walking: FNS-only (which retained a stiff knee during stance) and VIKM-HNP (which allowed controlled knee motion during stance). The stimulation pattern driving the walking motion remained the same for both techniques; the only difference was that knee extensor stimulation was constant during stance with FNS-only and modulated together with the VIKM to control knee motion during stance with VIKM-HNP.
Results
Stance phase knee angle was more natural during VIKM-HNP gait while knee hyperextension persisted during stiff-legged FNS-only walking. During loading response phase, vertical ground reaction force was less impulsive and instantaneous gait speed was increased with VIKM-HNP, suggesting that knee flexion assisted in weight transfer to the leading limb. Enhanced knee flexion during pre-swing phase also aided flexion during swing, especially when response to stimulation was compromised.
Conclusions
These results show the potential advantages of incorporating stance controlled knee flexion into a hybrid neuroprosthesis for walking. The addition of such control to FNS driven walking could also enable non-level walking tasks such as uneven terrain, slope navigation and stair descent where controlled knee flexion during weight bearing is critical.
doi:10.1186/1743-0003-10-68
PMCID: PMC3708761  PMID: 23826711
Functional neuromuscular stimulation; Hybrid neuroprosthesis; Controllable orthosis; Gait; Spinal cord injury; Gait; Exoskeleton
19.  Elastic coupling of limb joints enables faster bipedal walking 
The passive dynamics of bipedal limbs alone are sufficient to produce a walking motion, without need for control. Humans augment these dynamics with muscles, actively coordinated to produce stable and economical walking. Present robots using passive dynamics walk much slower, perhaps because they lack elastic muscles that couple the joints. Elastic properties are well known to enhance running gaits, but their effect on walking has yet to be explored. Here we use a computational model of dynamic walking to show that elastic joint coupling can help to coordinate faster walking. In walking powered by trailing leg push-off, the model's speed is normally limited by a swing leg that moves too slowly to avoid stumbling. A uni-articular spring about the knee allows faster but uneconomical walking. A combination of uni-articular hip and knee springs can speed the legs for improved speed and economy, but not without the swing foot scuffing the ground. Bi-articular springs coupling the hips and knees can yield high economy and good ground clearance similar to humans. An important parameter is the knee-to-hip moment arm that greatly affects the existence and stability of gaits, and when selected appropriately can allow for a wide range of speeds. Elastic joint coupling may contribute to the economy and stability of human gait.
doi:10.1098/rsif.2008.0415
PMCID: PMC2696144  PMID: 18957360
locomotion; biomechanics; dynamics; robotics; muscle; tendon
20.  Adaptive, Fast Walking in a Biped Robot under Neuronal Control and Learning 
PLoS Computational Biology  2007;3(7):e134.
Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (>3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks.
Author Summary
The problem of motor coordination of complex multi-joint movements has been recognized as very difficult in biological as well as in technical systems. The high degree of redundancy of such movements and the complexity of their dynamics make it hard to arrive at robust solutions. Biological systems, however, are able to move with elegance and efficiency, and they have solved this problem by a combination of appropriate biomechanics, neuronal control, and adaptivity. Human walking is a prominent example of this, combining dynamic control with the physics of the body and letting it interact with the terrain in a highly energy-efficient way during walking or running. The current study is the first to use a similar hybrid and adaptive, mechano–neuronal design strategy to build and control a small, fast biped walking robot and to make it learn to adapt to changes in the terrain to a certain degree. This study thus presents a proof of concept for a design principle suggested by physiological findings and may help us to better understand the interplay of these different components in human walking as well as in other complex movement patterns.
doi:10.1371/journal.pcbi.0030134
PMCID: PMC1914373  PMID: 17630828
21.  Neural control and adaptive neural forward models for insect-like, energy-efficient, and adaptable locomotion of walking machines 
Living creatures, like walking animals, have found fascinating solutions for the problem of locomotion control. Their movements show the impression of elegance including versatile, energy-efficient, and adaptable locomotion. During the last few decades, roboticists have tried to imitate such natural properties with artificial legged locomotion systems by using different approaches including machine learning algorithms, classical engineering control techniques, and biologically-inspired control mechanisms. However, their levels of performance are still far from the natural ones. By contrast, animal locomotion mechanisms seem to largely depend not only on central mechanisms (central pattern generators, CPGs) and sensory feedback (afferent-based control) but also on internal forward models (efference copies). They are used to a different degree in different animals. Generally, CPGs organize basic rhythmic motions which are shaped by sensory feedback while internal models are used for sensory prediction and state estimations. According to this concept, we present here adaptive neural locomotion control consisting of a CPG mechanism with neuromodulation and local leg control mechanisms based on sensory feedback and adaptive neural forward models with efference copies. This neural closed-loop controller enables a walking machine to perform a multitude of different walking patterns including insect-like leg movements and gaits as well as energy-efficient locomotion. In addition, the forward models allow the machine to autonomously adapt its locomotion to deal with a change of terrain, losing of ground contact during stance phase, stepping on or hitting an obstacle during swing phase, leg damage, and even to promote cockroach-like climbing behavior. Thus, the results presented here show that the employed embodied neural closed-loop system can be a powerful way for developing robust and adaptable machines.
doi:10.3389/fncir.2013.00012
PMCID: PMC3570936  PMID: 23408775
efference copy; central pattern generators; sensory feedback; recurrent neural networks; local leg control; walking gait; autonomous robots
22.  Unsteady locomotion: integrating muscle function with whole body dynamics and neuromuscular control 
The Journal of experimental biology  2007;210(Pt 17):2949-2960.
Summary
By integrating studies of muscle function with analysis of whole body and limb dynamics, broader appreciation of neuromuscular function can be achieved. Ultimately, such studies need to address non-steady locomotor behaviors relevant to animals in their natural environments. When animals move slowly they likely rely on voluntary coordination of movement involving higher brain centers. However, when moving fast, their movements depend more strongly on responses controlled at more local levels. Our focus here is on control of fast-running locomotion. A key observation emerging from studies of steady level locomotion is that simple spring-mass dynamics, which help to economize energy expenditure, also apply to stabilization of unsteady running. Spring-mass dynamics apply to conditions that involve lateral impulsive perturbations, sudden changes in terrain height, and sudden changes in substrate stiffness or damping. Experimental investigation of unsteady locomotion is challenging, however, due to the variability inherent in such behaviors. Another emerging principle is that initial conditions associated with postural changes following a perturbation define different context-dependent stabilization responses. Distinct stabilization modes following a perturbation likely result from proximo-distal differences in limb muscle architecture, function and control strategy. Proximal muscles may be less sensitive to sudden perturbations and appear to operate, in such circumstances, under feed-forward control. In contrast, multiarticular distal muscles operate, via their tendons, to distribute energy among limb joints in a manner that also depends on the initial conditions of limb contact with the ground. Intrinsic properties of these distal muscle–tendon elements, in combination with limb and body dynamics, appear to provide rapid initial stabilizing mechanisms that are often consistent with spring-mass dynamics. These intrinsic mechanisms likely help to simplify the neural control task, in addition to compensating for delays inherent to subsequent force- and length-dependent neural feedback. Future work will benefit from integrative biomechanical approaches that employ a combination of modeling and experimental techniques to understand how the elegant interplay of intrinsic muscle properties, body dynamics and neural control allows animals to achieve stability and agility over a variety of conditions.
doi:10.1242/jeb.005801
PMCID: PMC2651961  PMID: 17704070
EMG; force; muscle strain; spring-mass; work
23.  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.
doi:10.1098/rsif.2007.1095
PMCID: PMC2705974  PMID: 17594960
elephant; Proboscidea; locomotion; biomechanics; dynamics; gait
24.  Minimal percentage of dose received by 90% of the urethra (%UD90) is the most significant predictor of PSA bounce in patients who underwent low-dose-rate brachytherapy (LDR-brachytherapy) for prostate cancer 
BMC Urology  2012;12:28.
Background
To clarify the significant clinicopathological and postdosimetric parameters to predict PSA bounce in patients who underwent low-dose-rate brachytherapy (LDR-brachytherapy) for prostate cancer.
Methods
We studied 200 consecutive patients who received LDR-brachytherapy between July 2004 and November 2008. Of them, 137 patients did not receive neoadjuvant or adjuvant androgen deprivation therapy. One hundred and forty-two patients were treated with LDR-brachytherapy alone, and 58 were treated with LDR-brachytherapy in combination with external beam radiation therapy. The cut-off value of PSA bounce was 0.1 ng/mL. The incidence, time, height, and duration of PSA bounce were investigated. Clinicopathological and postdosimetric parameters were evaluated to elucidate independent factors to predict PSA bounce in hormone-naïve patients who underwent LDR-brachytherapy alone.
Results
Fifty patients (25%) showed PSA bounce and 10 patients (5%) showed PSA failure. The median time, height, and duration of PSA bounce were 17 months, 0.29 ng/mL, and 7.0 months, respectively. In 103 hormone-naïve patients treated with LDR-brachytherapy alone, and univariate Cox proportional regression hazard model indicated that age and minimal percentage of the dose received by 30% and 90% of the urethra were independent predictors of PSA bounce. With a multivariate Cox proportional regression hazard model, minimal percentage of the dose received by 90% of the urethra was the most significant parameter of PSA bounce.
Conclusions
Minimal percentage of the dose received by 90% of the urethra was the most significant predictor of PSA bounce in hormone-naïve patients treated with LDR-brachytherapy alone.
doi:10.1186/1471-2490-12-28
PMCID: PMC3487947  PMID: 22974428
Prostate cancer; Brachytherapy; PSA bounce; Post-dosimetry; UD90 (%)
25.  Identifying malaria vector breeding habitats with remote sensing data and terrain-based landscape indices in Zambia 
Background
Malaria, caused by the parasite Plasmodium falciparum, is a significant source of morbidity and mortality in southern Zambia. In the Mapanza Chiefdom, where transmission is seasonal, Anopheles arabiensis is the dominant malaria vector. The ability to predict larval habitats can help focus control measures.
Methods
A survey was conducted in March-April 2007, at the end of the rainy season, to identify and map locations of water pooling and the occurrence anopheline larval habitats; this was repeated in October 2007 at the end of the dry season and in March-April 2008 during the next rainy season. Logistic regression and generalized linear mixed modeling were applied to assess the predictive value of terrain-based landscape indices along with LandSat imagery to identify aquatic habitats and, especially, those with anopheline mosquito larvae.
Results
Approximately two hundred aquatic habitat sites were identified with 69 percent positive for anopheline mosquitoes. Nine species of anopheline mosquitoes were identified, of which, 19% were An. arabiensis. Terrain-based landscape indices combined with LandSat predicted sites with water, sites with anopheline mosquitoes and sites specifically with An. arabiensis. These models were especially successful at ruling out potential locations, but had limited ability in predicting which anopheline species inhabited aquatic sites. Terrain indices derived from 90 meter Shuttle Radar Topography Mission (SRTM) digital elevation data (DEM) were better at predicting water drainage patterns and characterizing the landscape than those derived from 30 m Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) DEM.
Conclusions
The low number of aquatic habitats available and the ability to locate the limited number of aquatic habitat locations for surveillance, especially those containing anopheline larvae, suggest that larval control maybe a cost-effective control measure in the fight against malaria in Zambia and other regions with seasonal transmission. This work shows that, in areas of seasonal malaria transmission, incorporating terrain-based landscape models to the planning stages of vector control allows for the exclusion of significant portions of landscape that would be unsuitable for water to accumulate and for mosquito larvae occupation. With increasing free availability of satellite imagery such as SRTM and LandSat, the development of satellite imagery-based prediction models is becoming more accessible to vector management coordinators.
doi:10.1186/1476-072X-9-58
PMCID: PMC2993656  PMID: 21050496

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