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About this book

The model-based investigation of motions of anthropomorphic systems is an important interdisciplinary research topic involving specialists from many fields such as Robotics, Biomechanics, Physiology, Orthopedics, Psychology, Neurosciences, Sports, Computer Graphics and Applied Mathematics. This book presents a study of basic locomotion forms such as walking and running is of particular interest due to the high demand on dynamic coordination, actuator efficiency and balance control. Mathematical models and numerical simulation and optimization techniques are explained, in combination with experimental data, which can help to better understand the basic underlying mechanisms of these motions and to improve them. Example topics treated in this book are

Modeling techniques for anthropomorphic bipedal walking systemsOptimized walking motions for different objective functionsIdentification of objective functions from measurementsSimulation and optimization approaches for humanoid robotsBiologically inspired control algorithms for bipedal walkingGeneration and deformation of natural walking in computer graphicsImitation of human motions on humanoidsEmotional body language during walking Simulation of biologically inspired actuators for bipedal walking machinesModeling and simulation techniques for the development of prosthesesFunctional electrical stimulation of walking.

Table of Contents


Trajectory-Based Dynamic Programming

We informally review our approach to using trajectory optimization to accelerate dynamic programming. Dynamic programming provides a way to design globally optimal control laws for nonlinear systems. However, the curse of dimensionality, the exponential dependence of memory and computation resources needed on the dimensionality of the state and control, limits the application of dynamic programming in practice. We explore trajectory-based dynamic programming, which combines many local optimizations to accelerate the global optimization of dynamic programming. We are able to solve problems with less resources than grid-based approaches, and to solve problems we couldn’t solve before using tabular or global function approximation approaches.

Christopher G. Atkeson, Chenggang Liu

Use of Compliant Actuators in Prosthetic Feet and the Design of the AMP-Foot 2.0

From robotic prostheses, to automated gait trainers, rehabilitation robots have one thing in common: they need actuation. The use of compliant actuators is currently growing in importance and has applications in a variety of robotic technologies where accurate trajectory tracking is not required like assistive technology or rehabilitation training. In this chapter, the authors presents the current state-ofthe- art in trans-tibial (TT) prosthetic devices using compliant actuation. After that, a detailed description is given of a new energy efficient below-knee prosthesis, the AMP-Foot 2.0.

Pierre Cherelle, Victor Grosu, Michael Van Damme, Bram Vanderborght, Dirk Lefeber

Modeling and Optimization of Human Walking

In this paper we show how optimal control techniques can be used to generate natural human walking motions in 3D. Our approach has potential applications in humanoid robotics, biomechanics and computer graphics. It has the advantage that it does not require any previous knowledge about walking motions from experiments. In this study we consider symmetric walking along a straight line, but the same techniques can be used to generate walking motions along curved paths or asymetric motions.We establish a multibody model of the human body with twelve segments including a head, a three-segment trunk, and arms and legs with two segments each. An optimal control problem is formulated that minimizes joint torques head movement, and the impulse on touch-down in a combined criterion. The dynamics of the multi-body system are considered as constraints to the optimal control problem to guarantee physically feasible motions. The optimal control problem is solved using an efficient direct multiple-shooting method. A skeletal animation library is used to present the results of the optimized motion.

Martin Felis, Katja Mombaur

Motion Generation with Geodesic Paths on Learnt Skill Manifolds

We present a framework for generating motions drawn from parametrized classes of motions and in response to goals chosen arbitrarily from a set. Our framework is based on learning a manifold representation of possible trajectories, from a set of example trajectories that are generated by a (computationally expensive) process of optimization. We show that these examples can be utilized to learn a manifold on which all feasible trajectories corresponding to a skill are the geodesics. This manifold is learned by inferring the local tangent spaces from data. Our main result is that this process allows us to define a flexible and computationally efficient motion generation procedure that comes close to the much more expensive computational optimization procedure in terms of accuracy while taking a small fraction of the time to perform a similar computation.

Ioannis Havoutis, Subramanian Ramamoorthy

Online CPG-Based Gait Monitoring and Optimal Control of the Ankle Joint for Assisted Walking in Hemiplegic Subjects

The paper introduces an approach to the FES-assisted correction of the drop-foot syndrome in post-stroke hemiplegic patients. The approach is based on a two stage architecture. One stage is dedicated to the online estimation of high-level gait information and the second to the generation of optimal ankle joint trajectories for walking assistance. The general gait information is obtained through the observation of one limb based on a central pattern generator model generating rhythmic trajectories which auto-adapt to real-measurements. This allows us to obtain information about the execution of the walking cycle. Optimal control is used to generate ankle joint dorsi-flexion trajectories during the swing phase of the corresponding deficient leg based on a muscle model and on the information provided by the first stage and some estimated or measured information about the controlled leg. This allows us to minimize a criteria linked to muscle activation, excitation or fatigue while satisfying constraints such as ground clearance, instead of just mimicking a priori chosen foot ankle trajectories which may be suboptimal. The strategy is validated in simulation using experimental data recorded in one healthy subject.

Rodolphe Héliot, Katja Mombaur, Christine Azevedo-Coste

The Combined Role of Motion-Related Cues and Upper Body Posture for the Expression of Emotions during Human Walking

The present study aimed at investigating how emotion affect the kinematic aspect of human walking. The gaits of eight professional actors expressing different types of emotions (neutral, joy, anger, sadness and fear) during walking were recorded and analyzed in the sagittal plane. We show both step-related behavioural changes (in terms of step length, speed,etc.) that are common to different emotions and emotion-specific body configuration changes (mainly at the level of the upper body posture) during emotional gaits. Since the overall speed of walking is another major variant in walking, natural walking at different speeds were recorded in another session for a control.

Halim Hicheur, Hideki Kadone, Julie Grèzes, Alain Berthoz

Whole Body Motion Control Framework for Arbitrarily and Simultaneously Assigned Upper-Body Tasks and Walking Motion

A walking motion of a humanoid has been analyzed or developed without considering motions of the remaining parts of the humanoid. In order to perform tasks in the human’s living environment, a walking motion and assigned tasks must be considered at the same time. In this paper, a whole body motion generation method, i.e., the motion embedded CoM Jacobian method is introduced. With the method, a balance control and assigned motions are separated and thus, the assigned motions can be generated without considering balance of a humanoid. As experimental examples, whole body motion of a humanoid is assigned by the tele-operation. Arbitrarily assigned upper body motions and independently generated walking motions are combined to generate a balanced whole body motion with the suggested methods.

Doik Kim, Bum-Jae You, Sang-Rok Oh

Structure Preserving Optimal Control of Three-Dimensional Compass Gait

The benefits of structure preserving algorithms for the numerical time-integration of mechanical systems, also called mechanical integrators, are widely accepted in forward dynamic simulations. However, in the field of motion planning and optimal control via direct methods, so far, these benefits have been less used. The dynamic optimisation method DMOC, does exploit the structure preserving properties of a variational integrator within an optimal control problem. This work considers the optimal control of a bipedal compass gait by modeling the double stance configuration as a transfer of contact constraints between the feet and the ground and develops a structure preserving simulation method for this context.

Sigrid Leyendecker, David Pekarek, Jerrold E. Marsden

Quasi-straightened Knee Walking for the Humanoid Robot

Most humanoid robots do not walk in a very human-like manner due to their style of bent knee walking. Typically for decoupling the motion in the sagittal and the coronal planes, the acceleration term in the zero moment point (ZMP) equation is set to zero, resulting in a constant height of the center of mass (COM). This constraint creates the bent knee profile that is fairly typical for walking robots,which particularly requires high torque transmission from motors. Hence, it is interesting to investigate an improved trajectory generator that produces a more straight knee walking which is more energy efficient and natural compared to those performed by the bent knee walking. This issue is addressed by adding a virtual spring-damper to the cart-table model. This strategy combines the preview control for generating the desired horizontal motions of the COM, and the virtual model for generating the vertical COM motion. The feasibility is evaluated by a mathematical investigation of the sensitivity of ZMP errors in MATLAB simulation of a multi-body humanoid model. The walking pattern is applied to the simulated humanoid iCub using the dynamic simulator OpenHRP3. The simulated iCub successfully performs walking gaits. Simulation results are presented and compared to the biomechanical study from human gaits. Both the knee joint torque and energy consumption of all joints required by the proposed strategy are reduced compared to that of the conventional cart-table scheme.

Zhibin Li, Bram Vanderborght, Nikos G. Tsagarakis, Darwin G. Caldwell

Modeling and Control of Dynamically Walking Bipedal Robots

Today’s bipedal robots still cannot compete with humans regarding efficiency, velocity, and robustness of locomotion. Thus, this paper suggests a control concept for dynamic walking based on insights into human motion control. Key features include exploitation of passive dynamics, hierarchical control, and reflexes, while not requiring a full dynamical model.Walking stability is achieved by a set of postural reflexes based on the motion of the extrapolated center of mass. It shows that only a small number of joints must be simultaneously actively actuated during the different phases of walking. Besides the control concept, the anthropomorphic biped model and its properties like compliant actuation are presented as they prove to be essential for the walking performance. Specifically, the approach requires non self-locking and torque-controllable joints with parallel elasticity and low friction, similar to the human muscle-tendon system. The approach is validated for 3D dynamic walking within a physical simulation framework. Results show an efficient, fluent, and fast gait that can cope with considerable disturbances. The resulting joint trajectories show significant resemblance to human walking data.

Tobias Luksch, Karsten Berns

In Humanoid Robots, as in Humans, Bipedal Standing Should Come before Bipedal Walking: Implementing the Functional Reach Test

This chapter describes a computational architecture for coordinating the degrees of freedom of the humanoid robot iCub during bipedal standing, with particular reference to the Whole Body Reaching and the Functional Reach Test.

Vishwanathan Mohan, Jacopo Zenzeri, Giorgio Metta, Pietro Morasso

A New Optimization Criterion Introducing the Muscle Stretch Velocity in the Muscular Redundancy Problem: A First Step into the Modeling of Spastic Muscle

Over the past few decades, musculo-skeletal modeling has been proposed as an in silico alternative to the invasive in vivo measurement of internal forces (e.g., musculo-tendon and joint reaction forces). However, even if great efforts have been made to improve the models, they remain partially validated and not adapted to pathologic subjects with orthopeadic and/or neurologic disorders. Indeed, even if a geometric scaling can be done using medical imaging techniques, the personalization of motor control specificities remains problematic. Consequently, when optimization techniques are used to solve the muscular redundancy problem, the selected criteria, that should reflect the motor control strategies, are not adapted to the gait disorders, such as muscle spasticity. The goal of this study was to introduce the muscle stretch velocity in the objective function, since muscle spasticity is linked to this parameter. We show that the maximization of the squared muscle stretch velocity provide more physiologic results during the stance phase and could be a way to introduce a spasticity criterion.

F. Moissenet, D. Pradon, N. Lampire, R. Dumas, L. Chèze

Forward and Inverse Optimal Control of Bipedal Running

This paper discusses forward and inverse optimal control problems for bipedal human-like running, with a focus on inverse optimal control. The (forward) optimal control problem looks for the optimal solution for a problem formulation, i.e. given objective function and given dynamic constraints. The inverse optimal control problem is more challenging and consists in determining the objective function and potentially unknown parts in the dynamic model that best reproduce a solution that is known from measurements. Periodic running motions are modeled as hybrid dynamic models with multiple phases and discontinuities, based on a three-dimensional multibody system model with 25 degrees of freedom.We investigate a recorded running motion on a treadmill at 10 km/h running speed and identify the best possible objective function based on some hypotheses for potential contributions to this objective function. For this, we apply a previously developed inverse optimal control technique which uses a combination of a direct multiple shooting method and a derivative-free optimization technique, and we demonstrate here that it also works for problems of the given complexity.

Katja Mombaur, Anne-Hélène Olivier, Armel Crétual

Synthesizing Human-Like Walking in Constrained Environments

We present a new algorithm to generate plausible walking motion for high-DOF human-like articulated figures in constrained environments with multiple obstacles. Our approach combines hierarchical model decomposition with sample-based planning to efficiently compute a collision-free path in tight spaces. Furthermore, we use path perturbation and replanning techniques to satisfy the kinematic and dynamic constraints on the motion. In order to generate realistic human-like motion, we present a new motion blending algorithm that refines the path computed by the planner with motion capture data to compute a smooth and plausible trajectory. We demonstrate the results of generating motion corresponding to placing or lifting object, walking and bending for a 34-DOF articulated model.

Jia Pan, Liangjun Zhang, Dinesh Manocha

Locomotion Synthesis for Digital Actors

Motion capture technologies are commonly used in the field of computer animation for interactive applications. They enable synthesizing highly realistic motions for human figures, but they suffer a lack of flexibility. Editing is required to answer the needs of interactivity, or to match the motion with some new geometrical and environmental constraints. During the last two decades, the computer animation research community expended a great deal of effort to use prerecorded sets of motion capture to synthesize animations with unknown (a priori) constraints. This paper provides a short overview on these recent motion capture edition techniques. We also describe more into details a method for synthesizing locomotion with continuous control over velocity parameters. We expect these previous works to be of interest for robotocists who attempt to control humanoid robots motion by imitation techniques, and who first need to be able to synthesize with control input motions.

Julien Pettré

Whole-Body Motion Synthesis with LQP-Based Controller – Application to iCub

This paper deals with the dynamic control of humanoid robots interacting with their environment, and more specifically the behavioral synthesis for dynamic tasks. The particular problem that is considered here is the sequencing of elementary activities subjected to physical constraints, both internal as torque limits and external as contacts, within the framework of posture/tasks coordination. For that we propose to convert the set of tasks into weighted quadratic functions and to minimize their cost with a Linear Quadratic Program. The combination of elementary tasks leads to complex actions, and the continuous evolution of the weights ensures smooth transitions over time, as it is shown in the results.

Joseph Salini, Sébastien Barthélemy, Philippe Bidaud, Vincent Padois

Walking and Running: How Leg Compliance Shapes the Way We Move

The function of the human leg during walking and running is complex. One issue is the segmented structure of the leg, which consists of thigh, shank and foot. The situation is further challenged by the parallel arrangement of muscles spanning a single or multiple leg joints. How is the leg function organized to make typical movements such as walking and running possible and easily accessible? In this paper, we review a number of biomechanical models based on the spring-mass model, which may help to better understand how compliant leg function can be used and properly adjusted to selected movement tasks. This includes the emergence and stabilization of walking and running patterns. One general characteristic of movements based on compliant leg function is the functional redundancy in the leg adjustment, i.e. at a given speed, walking or running can be achieved with different leg strategies. This principle of redundant leg adjustments fulfilling the same general goal of movement is a key for understanding the organization of human locomotion.

Andre Seyfarth, Susanne Lipfert, Jürgen Rummel, Moritz Maus, Daniel Maykranz

Modeling and Simulation of Walking with a Mobile Gait Rehabilitation System Using Markerless Motion Data

Research and development of gait rehabilitation systems and devices such as orthosis, prosthesis and wearable robots are complex processes in which simulation techniques are exploited in order to accelerate development process, reduce development costs, optimize the proposed solution, analyse the interaction between the system and human, etc. The modelling and simulation results can give valuable insights in the functionality of the system and directions for optimization and improvement of the researched system. Within the frame of the RoboWalker project a concept of a mobile robotic gait rehabilitation system, which will improve gait rehabilitation through several novel system features, was investigated. The system consists of a mobile platform with integrated active exoskeleton. In this paper, the modelling and simulation approaches utilized in designing and analysing the concept of mobile gait rehabilitation system are presented together with a novel markerless motion capture system that was used for collecting human motion data for simulation purposes.

S. Slavnić, A. Leu, D. Ristić-Durrant, A. Graeser

Optimization and Imitation Problems for Humanoid Robots

In this paper, the problems of humanoid robot motion optimization and human motion imitation by a humanoid robot are investigated. At first, we propose a unified framework for the optimization of humanoid robot motions. This framework is based on an efficient dynamics algorithmwhich allows the calculation of the gradient function with respect to the control parameters analytically. We show the efficiency of the framework through an example of smoothing a pre-calculated humanoid motion by minimizing the exerted torques, and at the same time improving the stability of the humanoid robot during the execution of the motion. Furthermore, we give insights into the problem of imitating human capture motions by a humanoid robot. We point out that the imitation problem can be formulated as an optimization problem under the constraints of physical limits and balance. The experimental results conducted on the humanoid robot HRP-2 have pointed out the efficiency of the framework of optimization to smooth humanoid robot motions and to generate imitated motions that preserve the salient characteristics of the original human captured motions. Moreover the experiments showed that the optimization procedure is well converging thanks to the analytical computation of the gradient function.

Wael Suleiman, Eiichi Yoshida, Fumio Kanehiro, Jean-Paul Laumond, André Monin

Motor Control and Spinal Pattern Generators in Humans

Spinal pattern generators can produce cyclic and acyclic muscular activation patterns. Here we introduce a model, which describes the interaction between spinal pattern generators and the musculoskeletal system. The behavior of thismodel will be demonstrated in three different examples, i.e. the reflexive behavior, the behavior during locomotion and during coupled arm movements. The results show that the model was capable of reproducing complex reflex patterns. For locomotion, it demonstrated the ability in adapting to changes and selecting appropriate afferents, so as to enable step-like motion to occur. Even phase transition during coupled arm movements could be described by themodel. Our results support the hypothesis, that depending on the movement task, humans are able to change the coupling within the spinal pattern generator, which provides an extremely effizient motor control strategy.

Heiko Wagner, Arne Wulf, Sook-Yee Chong, Thomas Wulf

Modeling Human-Like Joint Behavior with Mechanical and Active Stiffness

The bipedal locomotion has become a research topic of great interest over the last decades. Several groups have realized dynamic walking on afore known terrain. Our goal is to realize dynamicwalking and running in rough terrain. Beside the control of the highly dynamic and unstable motion, the actuator itself is still an open research topic. The main task of such an actuator is to supply the system with energy to compensate losses due to internal friction and environmental impact. In slow walking speeds this share is very low. Several so-called passive walkers have shown that there is no need for an actuator, if the energy loss is compensated by transforming potential energy into kinetic energy [13, 4]. But in more dynamic motions like running and jumping, however, a powerful actuator is essential.

Thomas Wahl, Karsten Berns

Geometry and Biomechanics for Locomotion Synthesis and Control

This paper summarizes two pieces of work related to human locomotion. The common hypothesis underlying these works is that human locomotion is characterized by, and possibly optimized to, the inherent mechanical and sensory-motor network structures. The first work investigates the effect of foot geometry on the walking speed and efficiency. Inspired from passive walk, we consider a foot shape with circular toe and heel segments, and optimize the gait for different toe and heel radii. We then compare the optimized gaits and demonstrate that round foot realizes faster and more efficient gaits. The second work focuses on the time delay of the human somatosensory reflex. Humans can walk robustly despite the tens of milliseconds of latency between the sensor input and motor output. To investigate how time delay affect the reflex model, we build somatosensory reflex models assuming different latency values and perform cross validation across multiple motions. The result shows that the network model using the physiologically realistic latency value better generalizes to a wide variety of motions, suggesting that the network is optimized to the inherent latency of the neural system.

Katsu Yamane


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