Exploring Passive Dynamics in Legged Locomotion

A common observation among legged animals is that they move their limbs differently as they change their speed. The observed distinct patterns of limb movement are usually referred to as different gaits. Experiments with humans and mammals have shown that switching between different gaits as locomotion speed changes, enables energetically more economical locomotion. However, it still remains unclear why animals with very different morphologies use similar gaits, where these gaits come from, and how they are related. This dissertation approaches these questions by exploring the natural passive dynamic motions of a range of simplified mechanical models of legged locomotion. Recent research has shown that a simple bipedal model with compliant legs and a single set of parameters can match ground reaction forces of both human walking and running. As first contribution of this dissertation, this concept is extended to quadrupeds. A unified model is developed to reproduce many quadrupedal gaits by only varying the initial states of a motion. In addition, the model parameters are optimized to match the experimental data of real horses, as measured by an instrumented treadmill. It is shown that the proposed model is able to not only create similar kinematic motion trajectories, but can also explain the ground reaction forces of real horses moving with different gaits. In order to reveal the mechanical contribution to gaits, the simplistic bipedal and quadrupedal models are then augmented to have passive swing leg motions by including torsional springs at the hip joints. Through a numerical continuation of periodic motions, this work shows that a wide range of gaits emerges from a simple bouncing-in-place motion starting with different footfall patterns. For both, bipedal and quadrupedal models, these gaits arise along one-dimensional manifolds of solutions with varying total energy. Through breaking temporal and spatial symmetries of the periodic motions, these manifolds bifurcate into distinct branches with various footfall sequences. That is, passive gaits are obtained as different oscillatory motions of a single mechanical system with a single set of parameters. By reproducing a variety of gaits as a manifestation of the passive dynamics of unified models, this work provides insights into the underlying dynamics of legged locomotion and may help design of more economical controllers for legged machines.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147585/1/ganzheny_1.pd

A Rule Based Biped Dynamic Walking

Dynamic walking approach has got its significance because of its energy efficiency in walking. Walking models are made using this approach which would consume energy as low as the energy required for human being walking. The basis of this dynamic walking is purely passive walking which takes no energy for walking. For a simple compass model passive walking can be achieved only for particular initial conditions (angular positions and velocities) which are found by trial and error or from previous experience.Various ways are derived to make the model walk on a level ground by supplying external energy through some means i.e torques at hip joint and ankle joints which is called active walking. Two approaches are available for active walking, one is creating virtual slope and then by applying equivalent torques at ankle and hip as the functions of virtual slope;other approach is using torsional springs and dampers at hip as well as ankles such that the torques are given in terms of springs' stiffness coefficient and damping coefficient. The stability is analyzed based on ZMP position. When ZMP of the system falls within the foot support area then system is said to be stable

Feedback Control Design for MARLO, a 3D-Bipedal Robot.

This work develops feedback controllers for bipedal walking in 3D on level ground, both in simulation and experimentally. MARLO is a new robot that has been designed for the study of 3D-bipedal locomotion, with the aim of combining energy efficiency, speed, and robustness with respect to natural terrain variations in a single platform. The robot is highly underactuated, having six actuators and, in single support, 13 degrees of freedom. Its sagittal plane dynamics are designed to embody the spring loaded inverted pendulum (SLIP), which has been shown to provide a dynamic model of the body center of mass during steady running gaits in a wide diversity of terrestrial animals. A detailed dynamic model is used to optimize walking gaits with respect to the cost of mechanical transport (cmt), a dimensionless measure of energetic efficiency. A feedback controller is designed that balances the robot during the quiet standing mode, and another feedback policy is developed such that the robot can take a transition step from quiet standing to walking. A feedback controller is designed that stabilizes steady-state 3D walking gaits, despite the high degree of underactuation of the robot. These controllers are combined through a state machine that handles switching among the three controllers controllers. In experiments on planarized (2D) and untethered (3D) versions of the robot with point feet and passive feet (prosthetic feet) walking over flat ground or on a ramp with a shallow slope, the adaptability of the designed controller to the environment (planar or untethered, flat ground or ramp), and to the morphology of the robot (point feet or passive feet), is demonstrated. In experiments on a planarized version of the robot with passive feet, the controller yielded stable walking after starting from quiet standing, autonomously and without any intervention from the operator. In experiments on an untethered (3D) version of the robot, the controller was able to balance the robot over flat ground or on a shallow ramp during the quiet standing mode. In addition, the controller yielded six-untethered ``human-like'' steps after starting from quiet standing, autonomously without any intervention from the operator.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102339/1/aramez_1.pd

Exploiting inherent robustness and natural dynamics in the control of bipedal walking robots

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (p. 115-120).Walking is an easy task for most humans and animals. Two characteristics which make it easy are the inherent robustness (tolerance to variation) of the walking problem and the natural dynamics of the walking mechanism. In this thesis we show how understanding and exploiting these two characteristics can aid in the control of bipedal robots. Inherent robustness allows for the use of simple, low impedance controllers. Natural dynamics reduces the requirements of the controller. We present a series of simple physical models of bipedal walking. The insight gained from these models is used in the development of three planar (motion only in the sagittal plane) control algorithms. The first uses simple strategies to control the robot to walk. The second exploits the natural dynamics of a kneecap, compliant ankle, and passive swing-leg. The third achieves fast swing of the swing-leg in order to enable the robot to walk quickly (1.25m). These algorithms are implemented on Spring Flamingo, a planar bipedal walking robot, which was designed and built for this thesis. Using these algorithms, the robot can stand and balance, start and stop walking, walk at a range of speeds, and traverse slopes and rolling terrain. Three-dimensional walking on flat ground is implemented and tested in simulation. The dynamics of the sagittal plane are sufficiently decoupled from the dynamics of the frontal and transverse planes such that control.-of each can be treated separately. We achieve three-dimensional walking by adding lateral balance to the planar algorithms. Tests of this approach on a real three-dimensional robot will lead to a more complete understanding of the control of bipedal walking in robots and humans.by Jerry E. Pratt.Ph.D

Energetics and Passive Dynamics of Quadruped Robot Planar Running Gaits

Quadruped robots find application in military for load carrying over uneven terrain, humanitarian de-mining, and search and rescue missions. The energy required for quadruped robot locomotion needs to be supplied from on-board energy source which can be either electrical batteries or fuels such as gasolene/diesel. The range and duration of missions very much depend on the amount of energy carried, which is highly limited. Hence, energy efficiency is of paramount importance in building quadruped robots. Study of energy efficiency in quadruped robots not only helps in efficient design of quadruped robots, but also helps understand the biomechanics of quadrupedal animals. This thesis focuses on the energy efficiency of planar running gaits and presents: (a) derivation of cost of transport expressions for trot and bounding gaits, (b) advantages of articulated torso over rigid torso for quadruped robot, (c) symmetry based control laws for passive dynamic bounding and design for inherent stability, and (d) effect of asymmetry in zero-energy bounding gaits

Bipedal Walking Analysis, Control, and Applications Towards Human-Like Behavior

Realizing the essentials of bipedal walking balance is one of the core studies in both robotics and biomechanics. Although the recent developments of walking control on bipedal robots have brought the humanoid automation to a different level, the walking performance is still limited compared to human walking, which also restricts the related applications in biomechanics and rehabilitation. To mitigate the discrepancy between robotic walking and human walking, this dissertation is broken into three parts to develop the control methods to improve three important perspectives: predictive walking behavior, gait optimization, and stepping strategy. To improve the predictive walking behavior captured by the model predictive control (MPC) which is transitionally applied with the nonlinear tracking control in sequence, a quadratic program (QP)-based controller is proposed to unify center of mass (COM) planning using MPC and a nonlinear torque control with control Lyapunov function (CLF). For the gait optimization, we focus on the algorithms of trajectory optimization with direct collocation framework. We propose a robust trajectory optimization using step-time sampling for a simple walker under terrain uncertainties. Towards generating human-like walking gait with multi-domain (phases), we improve the optimization through contact with more accurate transcription method for level walking, and generalize the hybrid zero dynamics (HZD) gait optimization with modified contact conditions for walking on various terrains. The results are compared with human walking gaits, where the similar trends and the sources of discrepancies are identified. In the third part for stepping strategy, we perform step estimation based on capture point (CP) for different human movements, including single-step (balance) recovery, walking and walking with slip. The analysis provides the insights of the efficacy and limitation of CP-based step estimation for human gait

Towards energy-efficient limit-cycle walking in biped service robots: design analysis, modeling and experimental study of biped robot actuated by linear motors

Researchers have been studying biped robots for many years, and, while many advances in the field have been accomplished, there still remain the challenge to transfer the existing solutions into real applications. The main issues are related to mobility and autonomy. In mobility, biped robots have evolved greatly, nevertheless they are still far from what a human can do in the work-site. Similarly, autonomy of biped platforms has been tackled on several different grounds, but its core problem still remains, and it is associated to energy issues. Because of these energy issues, lately the main attention has been redirected to the long term autonomy of the biped robotics platforms. For that, much effort has been made to develop new more energy-efficient biped robots. The GIMBiped project in Aalto University was established to tackle the previous issues in energy efficiency and mobility, through the study and implementation of dynamic and energy-efficient bipedal robotic waking. This thesis falls into the first studies needed to achieve the previous goal using the GIMBiped testbed, starting with a detailed analysis of the nonlinear dynamics of the target system, using a modeling and simulation tools. This work also presents an assessment of different control techniques based on Limit Cycle walking, carried out on a two-dimensional kneed bipedal simulator. Furthermore, a numerical continuation analysis of the mechanical parameters of the first GIMBiped prototype was performed, using the same approximated planar kneed biped model. This study is done to analyze the effect that such variations in the mechanical design parameters produce in the stability and energy-efficiency of the system.Finally, experiments were performed in the GIMBiped testbed. These experiments show the results of a hybrid control technique proposed by the author, which combines traditional ZMP-based walking approach with a Limit Cycle trajectory-following control. Furthermore the results of a pure ZMP-based type of control are also presented.

ATRIAS 1.0 & 2.1 : enabling agile biped locomotion with a template-driven approach to robot design

Practical bipedal robots need to be simultaneously efficient, robust, and versatile machines, but designing robots dynamically capable of these demands has been a significant bottleneck. We designed ATRIAS to be a highly dynamic biped capable of both walking and running untethered in real environments. To meet these goals, ATRIAS is designed to approximate dynamically capable locomotion template, i.e. the spring-mass model. We enumerate the challenges of this template-driven design approach and our solutions to make ATRIAS a real-world-viable human-scale machine. We show that ATRIAS exhibits behaviors predicted by spring-mass models in fulfillment of our design approach. Particularly, ATRIAS reproduces the characteristic ground-reaction forces of human walking and running, a key dynamical feature of spring-mass locomotion. We also demonstrate ATRIAS' capacity to walk, hop on one leg, bound like a spring-mass hopper, and recover from an unseen plunge into a 6.5-inch-deep gravel pit. Further, by building efficient spring-mass dynamics into the mechanical system, ATRIAS, when pushed, walks several steps without its actuators replenishing lost mechanical energy. These combined hardware experiments validate ATRIAS' capability as a platform for spring-mass robot controllers and for agile and economical locomotion in general. This thesis is the combination of two journal papers that focus on the ATRIAS robot that focus on statements in the above paragraph. It also includes a summary of the objectives and considerations that went into the design, manufacture and testing phases of the robots. This includes the project deliverables and deadlines, methods for building these robots, control theory considerations for ATRIAS, engineering objectives and questions addressed by this work

A Foot Placement Strategy for Robust Bipedal Gait Control

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance