Orbit Characterization, Stabilization and Composition on 3D Underactuated Bipedal Walking via Hybrid Passive Linear Inverted Pendulum Model

A Hybrid passive Linear Inverted Pendulum (H-LIP) model is proposed for characterizing, stabilizing and composing periodic orbits for 3D underactuated bipedal walking. Specifically, Period-l (P1) and Period -2 (P2) orbits are geometrically characterized in the state space of the H-LIP. Stepping controllers are designed for global stabilization of the orbits. Valid ranges of the gains and their optimality are derived. The optimal stepping controller is used to create and stabilize the walking of bipedal robots. An actuated Spring-loaded Inverted Pendulum (aSLIP) model and the underactuated robot Cassie are used for illustration. Both the aSLIP walking with PI or P2 orbits and the Cassie walking with all 3D compositions of the PI and P2 orbits can be smoothly generated and stabilized from a stepping-in-place motion. This approach provides a perspective and a methodology towards continuous gait generation and stabilization for 3D underactuated walking robots

Symmetry Method for Limit Cycle Walking of Legged Robots.

Dynamic steady-state walking or running gaits for legged robots correspond to periodic orbits in the dynamic model. The common method for obtaining such periodic orbits is conducting a numerical search for fixed points of a Poincare map. However, as the number of degrees of freedom of the robot grows, such numerical search becomes computationally expensive because in each search trial the dynamic equations need to be integrated. Moreover, the numerical search for periodic orbits is in general sensitive to model errors, and it remains to be seen if the periodic orbit which is the outcome of the search in the domain of the dynamic model corresponds to a periodic gait in the actual robot. To overcome these issues, we have presented the Symmetry Method for Limit Cycle Walking, which relaxes the need to search for periodic orbits, and at the same time, the limit cycles obtained with this method are robust to model errors. Mathematically, we describe the symmetry method in the context of so-called Symmetric Hybrid Systems, whose properties are discussed. In particular, it is shown that a symmetric hybrid system can have an infinite number of periodic orbits that can be identified easily. In addition, it is shown how control strategies need to be selected so that the resulting reduced order system still possesses the properties of a symmetric hybrid system. The method of symmetry for limit cycle walking is successfully tested on a 12-DOF 3D model of the humanoid robot Romeo.PhDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133356/1/razavi_1.pd

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Omnidirectional Walking Pattern Generator Combining Virtual Constraints and Preview Control for Humanoid Robots

This paper presents a novel omnidirectional walking pattern generator for bipedal locomotion combining two structurally different approaches based on the virtual constraints and the preview control theories to generate a flexible gait that can be modified on-line. The proposed strategy synchronizes the displacement of the robot along the two planes of walking: the zero moment point based preview control is responsible for the lateral component of the gait, while the sagittal motion is generated by a more dynamical approach based on virtual constraints. The resulting algorithm is characterized by a low computational complexity and high flexibility, requisite for a successful deployment to humanoid robots operating in real world scenarios. This solution is motivated by observations in biomechanics showing how during a nominal gait the dynamic motion of the human walk is mainly generated along the sagittal plane. We describe the implementation of the algorithm and we detail the strategy chosen to enable omnidirectionality and on-line gait tuning. Finally, we validate our strategy through simulation experiments using the COMAN + platform, an adult size humanoid robot developed at Istituto Italiano di Tecnologia. Finally, the hybrid walking pattern generator is implemented on real hardware, demonstrating promising results: the WPG trajectories results in open-loop stable walking in the absence of external disturbances

Rich and Robust Bio-Inspired Locomotion Control for Humanoid Robots

Bipedal locomotion is a challenging task in the sense that it requires to maintain dynamic balance while steering the gait in potentially complex environments. Yet, humans usually manage to move without any apparent difficulty, even on rough terrains. This requires a complex control scheme which is far from being understood. In this thesis, we take inspiration from the impressive human walking capabilities to design neuromuscular controllers for humanoid robots. More precisely, we control the robot motors to reproduce the action of virtual muscles commanded by stimulations (i.e. neural signals), similarly to what is done during human locomotion. Because the human neural circuitry commanding these muscles is not completely known, we make hypotheses about this control scheme to simplify it and progressively refine the corresponding rules. This thesis thus aims at developing new walking algorithms for humanoid robots in order to obtain fast, human-like and energetically efficient gaits. In particular, gait robustness and richness are two key aspects of this work. In other words, the gaits developed in the thesis can be steered by an external operator, while being resistant to external perturbations. This is mainly tested during blind walking experiments on COMAN, a 95 cm tall humanoid robot. Yet, the proposed controllers can be adapted to other humanoid robots. In the beginning of this thesis, we adapt and port an existing reflex-based neuromuscular model to the real COMAN platform. When tested in a 2D simulation environment, this model was capable of reproducing stable human-like locomotion. By porting it to real hardware, we show that these neuromuscular controllers are viable solutions to develop new controllers for robotics locomotion. Starting from this reflex-based model, we progressively iterate and transform the stimulation rules to add new features. In particular, gait modulation is obtained with the inclusion of a central pattern generator (CPG), a neural circuit capable of producing rhythmic patterns of neural activity without receiving rhythmic inputs. Using this CPG, the 2D walker controllers are incremented to generate gaits across a range of forward speeds close to the normal human one. By using a similar control method, we also obtain 2D running gaits whose speed can be controlled by a human operator. The walking controllers are later extended to 3D scenarios (i.e. no motion constraint) with the capability to adapt both the forward speed and the heading direction (including steering curvature). In parallel, we also develop a method to automatically learn stimulation networks for a given task and we study how flexible feet affect the gait in terms of robustness and energy efficiency. In sum, we develop neuromuscular controllers generating human-like gaits with steering capabilities. These controllers recruit three main components: (i) virtual muscles generating torque references at the joint level, (ii) neural signals commanding these muscles with reflexes and CPG signals, and (iii) higher level commands controlling speed and heading. Interestingly, these developments target humanoid robots locomotion but can also be used to better understand human locomotion. In particular, the recruitment of a CPG during human locomotion is still a matter open to debate. This question can thus benefit from the experiments performed in this thesis

Humanoid Robots

For many years, the human being has been trying, in all ways, to recreate the complex mechanisms that form the human body. Such task is extremely complicated and the results are not totally satisfactory. However, with increasing technological advances based on theoretical and experimental researches, man gets, in a way, to copy or to imitate some systems of the human body. These researches not only intended to create humanoid robots, great part of them constituting autonomous systems, but also, in some way, to offer a higher knowledge of the systems that form the human body, objectifying possible applications in the technology of rehabilitation of human beings, gathering in a whole studies related not only to Robotics, but also to Biomechanics, Biomimmetics, Cybernetics, among other areas. This book presents a series of researches inspired by this ideal, carried through by various researchers worldwide, looking for to analyze and to discuss diverse subjects related to humanoid robots. The presented contributions explore aspects about robotic hands, learning, language, vision and locomotion

Scaled Autonomy for Networked Humanoids

Humanoid robots have been developed with the intention of aiding in environments designed for humans. As such, the control of humanoid morphology and effectiveness of human robot interaction form the two principal research issues for deploying these robots in the real world. In this thesis work, the issue of humanoid control is coupled with human robot interaction under the framework of scaled autonomy, where the human and robot exchange levels of control depending on the environment and task at hand. This scaled autonomy is approached with control algorithms for reactive stabilization of human commands and planned trajectories that encode semantically meaningful motion preferences in a sequential convex optimization framework. The control and planning algorithms have been extensively tested in the field for robustness and system verification. The RoboCup competition provides a benchmark competition for autonomous agents that are trained with a human supervisor. The kid-sized and adult-sized humanoid robots coordinate over a noisy network in a known environment with adversarial opponents, and the software and routines in this work allowed for five consecutive championships. Furthermore, the motion planning and user interfaces developed in the work have been tested in the noisy network of the DARPA Robotics Challenge (DRC) Trials and Finals in an unknown environment. Overall, the ability to extend simplified locomotion models to aid in semi-autonomous manipulation allows untrained humans to operate complex, high dimensional robots. This represents another step in the path to deploying humanoids in the real world, based on the low dimensional motion abstractions and proven performance in real world tasks like RoboCup and the DRC