Compact analysis of 3D bipedal gait using geometric dynamics of simplified models

The large number of degrees of freedom in legged robots give rise to complicated dynamics equations. Analyzing these equations or using them for control can therefore be a difficult and non-intuitive task. A simplification of the complex multi-body dynamics can be achieved by instantaneously re- ducing it to an equivalent single inertial entity called the locked inertia or the composite rigid body inertia. In this paper, we adopt the methods of geometric dynamics to analyze the gait using the locked inertia of the robot. The analysis includes the rolling of a biped on a 3D rigid foot and 3D impacts. An example of numerical optimization of foot shape parameters is shown. Our long-term objective is to develop the theoretical frame- work and to provide the necessary tools for systematic analysis, design, and control of efficient biped robots

Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot

This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints and hybrid zero dynamics, in order to simultaneously compute a periodic orbit and an autonomous feedback controller that realizes the orbit. This method allows the computations to be carried out on a 2-DOF subsystem of the 8-DOF robot model. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincar\'e map of the hybrid zero dynamics. Three strategies are explored. The first strategy consists of imposing a stability condition during the search of a periodic gait by optimization. The second strategy uses an event-based controller. In the third approach, the effect of output selection is discussed and a pertinent choice of outputs is proposed, leading to stabilization without the use of a supplemental event-based controller

Optimization-based Framework for Stability and Robustness of Bipedal Walking Robots

As robots become more sophisticated and move out of the laboratory, they need to be able to reliably traverse difficult and rugged environments. Legged robots -- as inspired by nature -- are most suitable for navigating through terrain too rough or irregular for wheels. However, control design and stability analysis is inherently difficult since their dynamics are highly nonlinear, hybrid (mixing continuous dynamics with discrete impact events), and the target motion is a limit cycle (or more complex trajectory), rather than an equilibrium. For such walkers, stability and robustness analysis of even stable walking on flat ground is difficult. This thesis proposes new theoretical methods to analyse the stability and robustness of periodic walking motions. The methods are implemented as a series of pointwise linear matrix inequalities (LMI), enabling the use of convex optimization tools such as sum-of-squares programming in verifying the stability and robustness of the walker. To ensure computational tractability of the resulting optimization program, construction of a novel reduced coordinate system is proposed and implemented. To validate theoretic and algorithmic developments in this thesis, a custom-built “Compass gait” walking robot is used to demonstrate the efficacy of the proposed methods. The hardware setup, system identification and walking controller are discussed. Using the proposed analysis tools, the stability property of the hardware walker was successfully verified, which corroborated with the computational results

Coordinate transformation as a help for controller design in walking robots

For walking robots, the robot’s absolute position must be re- flected in the state. Usually one chooses to include the pose and velocity of the torso in the state (i.e., the torso is taken as the reference body). However, sometimes it is useful to choose a different reference body; in particular the stance foot is a good choice

Climbing and Walking Robots

With the advancement of technology, new exciting approaches enable us to render mobile robotic systems more versatile, robust and cost-efficient. Some researchers combine climbing and walking techniques with a modular approach, a reconfigurable approach, or a swarm approach to realize novel prototypes as flexible mobile robotic platforms featuring all necessary locomotion capabilities. The purpose of this book is to provide an overview of the latest wide-range achievements in climbing and walking robotic technology to researchers, scientists, and engineers throughout the world. Different aspects including control simulation, locomotion realization, methodology, and system integration are presented from the scientific and from the technical point of view. This book consists of two main parts, one dealing with walking robots, the second with climbing robots. The content is also grouped by theoretical research and applicative realization. Every chapter offers a considerable amount of interesting and useful information

Magnetorheological Variable Stiffness Robot Legs for Improved Locomotion Performance

In an increasingly automated world, interest in the field of robotics is surging, with an exciting branch of this area being legged robotics. These biologically inspired robots have leg-like limbs which enable locomotion, suited to challenging terrains which wheels struggle to conquer. While it has been quite some time since the idea of a legged machine was first made a reality, this technology has been modernised with compliant legs to improve locomotion performance. Recently, developments in biological science have uncovered that humans and animals alike control their leg stiffness, adapting to different locomotion conditions. Furthermore, as these studies highlighted potential to improve upon the existing compliant-legged robots, modern robot designs have seen implementation of variable stiffness into their legs. As this is quite a new concept, few works have been published which document such designs, and hence much potential exists for research in this area. As a promising technology which can achieve variable stiffness, magnetorheological (MR) smart materials may be ideal for use in robot legs. In particular, recent advances have enabled the use of MR fluid (MRF) to facilitate variable stiffness in a robust manner, in contrast to MR elastomer (MRE). Developed in this thesis is what was at the time the first rotary MR damper variable stiffness mechanism. This is proposed by the author for use within a robot leg to enable rapid stiffness control during locomotion. Based its mechanics and actuation, the leg is termed the magnetorheological variable stiffness actuator leg mark-I (MRVSAL-I). The leg, with a C-shaped morphology suited to torque actuation is first characterised through linear compression testing, demonstrating a wide range of stiffness variation. This variation is in response to an increase in electric current supplied to the internal electromagnetic coils of the MR damper. A limited degrees-of-freedom (DOF) bipedal locomotion platform is designed and manufactured to study the locomotion performance resulting from the variable stiffness leg. It is established that optimal stiffness tuning of the leg could achieve reduced mechanical cost of transport (MCOT), thereby improving locomotion performance. Despite the advancements to locomotion demonstrated, some design issues with the leg required further optimisation and a new leg morphology