Modular Hopping and Running via Parallel Composition

Though multi-functional robot hardware has been created, the complexity in its functionality has been constrained by a lack of algorithms that appropriately manage flexible and autonomous reconfiguration of interconnections to physical and behavioral components. Raibert pioneered a paradigm for the synthesis of planar hopping using a composition of ``parts\u27\u27: controlled vertical hopping, controlled forward speed, and controlled body attitude. Such reduced degree-of-freedom compositions also seem to appear in running animals across several orders of magnitude of scale. Dynamical systems theory can offer a formal representation of such reductions in terms of ``anchored templates,\u27\u27 respecting which Raibert\u27s empirical synthesis (and the animals\u27 empirical performance) can be posed as a parallel composition. However, the orthodox notion (attracting invariant submanifold with restriction dynamics conjugate to a template system) has only been formally synthesized in a few isolated instances in engineering (juggling, brachiating, hexapedal running robots, etc.) and formally observed in biology only in similarly limited contexts. In order to bring Raibert\u27s 1980\u27s work into the 21st century and out of the laboratory, we design a new family of one-, two-, and four-legged robots with high power density, transparency, and control bandwidth. On these platforms, we demonstrate a growing collection of $\{$body, behavior$\}$ pairs that successfully embody dynamical running / hopping ``gaits\u27\u27 specified using compositions of a few templates, with few parameters and a great deal of empirical robustness. We aim for and report substantial advances toward a formal notion of parallel composition---embodied behaviors that are correct by design even in the presence of nefarious coupling and perturbation---using a new analytical tool (hybrid dynamical averaging). With ideas of verifiable behavioral modularity and a firm understanding of the hardware tools required to implement them, we are closer to identifying the components required to flexibly program the exchange of work between machines and their environment. Knowing how to combine and sequence stable basins to solve arbitrarily complex tasks will result in improved foundations for robotics as it goes from ad-hoc practice to science (with predictive theories) in the next few decades

Agile Bipedal Locomotion via Hierarchical Control by Incorporating Physical Principles, Learning, and Optimization

Robotic Bipedal locomotion holds the potential for efficient, robust traversal of difficult terrain. The difficulty lies in the dynamics of locomotion which complicate control and motion planning. Bipedal locomotion dynamics are dimensionally large problems, extremely nonlinear, and operate on the limits of actuator capabilities, which limit the performance of generic methods of control. This thesis presents an approach to the problem of agile legged locomotion founded on a first principles understanding of gait dynamics. This approach is built on the perspective that an understanding of locomotion is vital to the successful application of modern control and planning tools. We present 1) a ground-up analysis of legged locomotion as a dynamical phenomenon, 2) approaches that utilize dynamically meaningful reduced order models of locomotion, and 3) applications to the hardware robot Cassie via reinforcement learning

Actuation-Aware Simplified Dynamic Models for Robotic Legged Locomotion

In recent years, we witnessed an ever increasing number of successful hardware implementations of motion planners for legged robots. If one common property is to be identified among these real-world applications, that is the ability of online planning. Online planning is forgiving, in the sense that it allows to relentlessly compensate for external disturbances of whatever form they might be, ranging from unmodeled dynamics to external pushes or unexpected obstacles and, at the same time, follow user commands. Initially replanning was restricted only to heuristic-based planners that exploit the low computational effort of simplified dynamic models. Such models deliberately only capture the main dynamics of the system, thus leaving to the controllers the issue of anchoring the desired trajectory to the whole body model of the robot. In recent years, however, we have seen a number of new approaches attempting to increase the accuracy of the dynamic formulation without trading-off the computational efficiency of simplified models. In this dissertation, as an example of successful hardware implementation of heuristics and simplified model-based locomotion, I describe the framework that I developed for the generation of an omni-directional bounding gait for the HyQ quadruped robot. By analyzing the stable limit cycles for the sagittal dynamics and the Center of Pressure (CoP) for the lateral stabilization, the described locomotion framework is able to achieve a stable bounding while adapting to terrains of mild roughness and to sudden changes of the user desired linear and angular velocities. The next topic reported and second contribution of this dissertation is my effort to formulate more descriptive simplified dynamic models, without trading off their computational efficiency, in order to extend the navigation capabilities of legged robots to complex geometry environments. With this in mind, I investigated the possibility of incorporating feasibility constraints in these template models and, in particular, I focused on the joint torques limits which are usually neglected at the planning stage. In this direction, the third contribution discussed in this thesis is the formulation of the so called actuation wrench polytope (AWP), defined as the set of feasible wrenches that an articulated robot can perform given its actuation limits. Interesected with the contact wrench cone (CWC), this yields a new 6D polytope that we name feasible wrench polytope (FWP), defined as the set of all wrenches that a legged robot can realize given its actuation capabilities and the friction constraints. Results are reported where, thanks to efficient computational geometry algorithms and to appropriate approximations, the FWP is employed for a one-step receding horizon optimization of center of mass trajectory and phase durations given a predefined step sequence on rough terrains. For the sake of reachable workspace augmentation, I then decided to trade off the generality of the FWP formulation for a suboptimal scenario in which a quasi-static motion is assumed. This led to the definition of the, so called, local/instantaneous actuation region and of the global actuation/feasible region. They both can be seen as different variants of 2D linear subspaces orthogonal to gravity where the robot is guaranteed to place its own center of mass while being able to carry its own body weight given its actuation capabilities. These areas can be intersected with the well known frictional support region, resulting in a 2D linear feasible region, thus providing an intuitive tool that enables the concurrent online optimization of actuation consistent CoM trajectories and target foothold locations on rough terrains

From walking to running: robust and 3D humanoid gait generation via MPC

Humanoid robots are platforms that can succeed in tasks conceived for humans. From locomotion in unstructured environments, to driving cars, or working in industrial plants, these robots have a potential that is yet to be disclosed in systematic every-day-life applications. Such a perspective, however, is opposed by the need of solving complex engineering problems under the hardware and software point of view. In this thesis, we focus on the software side of the problem, and in particular on locomotion control. The operativity of a legged humanoid is subordinate to its capability of realizing a reliable locomotion. In many settings, perturbations may undermine the balance and make the robot fall. Moreover, complex and dynamic motions might be required by the context, as for instance it could be needed to start running or climbing stairs to achieve a certain location in the shortest time. We present gait generation schemes based on Model Predictive Control (MPC) that tackle both the problem of robustness and tridimensional dynamic motions. The proposed control schemes adopt the typical paradigm of centroidal MPC for reference motion generation, enforcing dynamic balance through the Zero Moment Point condition, plus a whole-body controller that maps the generated trajectories to joint commands. Each of the described predictive controllers also feature a so-called stability constraint, preventing the generation of diverging Center of Mass trajectories with respect to the Zero Moment Point. Robustness is addressed by modeling the humanoid as a Linear Inverted Pendulum and devising two types of strategies. For persistent perturbations, a way to use a disturbance observer and a technique for constraint tightening (to ensure robust constraint satisfaction) are presented. In the case of impulsive pushes instead, techniques for footstep and timing adaptation are introduced. The underlying approach is to interpret robustness as a MPC feasibility problem, thus aiming at ensuring the existence of a solution for the constrained optimization problem to be solved at each iteration in spite of the perturbations. This perspective allows to devise simple solutions to complex problems, favoring a reliable real-time implementation. For the tridimensional locomotion, on the other hand, the humanoid is modeled as a Variable Height Inverted Pendulum. Based on it, a two stage MPC is introduced with particular emphasis on the implementation of the stability constraint. The overall result is a gait generation scheme that allows the robot to overcome relatively complex environments constituted by a non-flat terrain, with also the capability of realizing running gaits. The proposed methods are validated in different settings: from conceptual simulations in Matlab to validations in the DART dynamic environment, up to experimental tests on the NAO and the OP3 platforms

Climbing and Walking Robots

Nowadays robotics is one of the most dynamic fields of scientific researches. The shift of robotics researches from manufacturing to services applications is clear. During the last decades interest in studying climbing and walking robots has been increased. This increasing interest has been in many areas that most important ones of them are: mechanics, electronics, medical engineering, cybernetics, controls, and computers. Today’s climbing and walking robots are a combination of manipulative, perceptive, communicative, and cognitive abilities and they are capable of performing many tasks in industrial and non- industrial environments. Surveillance, planetary exploration, emergence rescue operations, reconnaissance, petrochemical applications, construction, entertainment, personal services, intervention in severe environments, transportation, medical and etc are some applications from a very diverse application fields of climbing and walking robots. By great progress in this area of robotics it is anticipated that next generation climbing and walking robots will enhance lives and will change the way the human works, thinks and makes decisions. This book presents the state of the art achievments, recent developments, applications and future challenges of climbing and walking robots. These are presented in 24 chapters by authors throughtot the world The book serves as a reference especially for the researchers who are interested in mobile robots. It also is useful for industrial engineers and graduate students in advanced study

Mechanisms for human balancing of an inverted pendulum using the ankle strategy

Maintenance of upright, human balance is neurologically and biomechanically a complex process, though the ankle strategy predominates in quiet standing. This investigation seeks insight into the complex problem by studying a reduced, yet related problem of how the ankle mechanisms are used to balance a human proportioned inverted pendulum. A distinguishing feature of the task is that despite one's best efforts to control this unstable load some irreducible sway always remains. Contrary to published ideas, modulation of effective ankle stiffness was not the way that sway size was altered. Rather, position was controlled by an intermittent, neurally modulated, ballistic-like pattern of torque whose anticipatory accuracy was improved to reduce sway size. Using a model, and by direct measurement, I found the intrinsic mechanical ankle stiffness will only partially counter the "gravitational spring". Since this stiffness was substantially constant and cannot be neurally modulated, I attribute it to the foot, tendon and aponeurosis rather than the activated calf muscle fibres. Thus triceps-surae muscles maintain balance via a spring-like element which is itself generally too compliant to provide even minimal stability. I hypothesise that balance is maintained by anticipatory, ballistic-like, biasing of the series-elastic element resulting from intermittent modulation of the triceps-surae

A Generalized Method for Predictive Simulation-Based Lower Limb Prosthesis Design

Lower limb prostheses are designed to replace the functions and form of the missing biological anatomy. These functions are hypothesized to improve user outcome measures which are negatively affected by receiving an amputation – such as metabolic cost of transport, preferred walking speed, and perceived discomfort during walking. However, the effect of these design functions on the targeted outcome measures is highly variable, suggesting that these relationships are not fully understood. Biomechanics simulation and modeling tools are increasingly capable of analyzing the effects of a design on the resulting user gait. In this work, prothesis-aided gait is optimized in simulation to reduce both muscle effort and peak loads on the residual limb using a generalized prosthesis model. Compared to a traditional revolute powered ankle joint model, a two degree-of freedom generalized model reduced muscle activations by 50% and peak loads by 15%. Simulated prosthesis behaviors corresponding to the optimal gait patterns were translated into a two degree-of-freedom ankle-foot prosthesis design with powered bidirectional linear translation and plantarflexion. The prototype is capable of delivering up to 171 N-m of plantarflexion torque and 499 N of translation force, with 15° dorsi-/35° plantarflexion and 10 cm translation range of motion. The mass and height of the ankle-foot are 2.29 kg and 19.5 cm, respectively. The mass of the entire system including the wearable offboard system is 8.58 kg. This platform is designed to emulate the behavior of the simulated prosthesis, as well as be configurable to emulate alternate behaviors obtained from simulations with different optimization objectives. The prototype is controlled to replicate simulated walking patterns using a high level finite state controller, mid-level stiffness controller, and low level load controller. Closed loop load control has bandwidth of 15 Hz in translation and 7.2 Hz in flexion. Load tracking during walking with a single able-bodied human subject ranges from 93 to 159 N in translation and 4.6 to 21.3 N-m in flexion. The contribution of this work is to provide a framework for predictive simulation-based prosthesis design, evidence of its practical implementation, and the experimental tools to validate future predictive simulation studies

Data-Driven Methods to Build Robust Legged Robots

For robots to ever achieve signicant autonomy, they need to be able to mitigate performance loss due to uncertainty, typically from a novel environment or morphological variation of their bodies. Legged robots, with their complex dynamics, are particularly challenging to control with principled theory. Hybrid events, uncertainty, and high dimension are all confounding factors for direct analysis of models. On the other hand, direct data-driven methods have proven to be equally dicult to employ. The high dimension and mechanical complexity of legged robots have proven challenging for hardware-in-the-loop strategies to exploit without signicant eort by human operators. We advocate that we can exploit both perspectives by capitalizing on qualitative features of mathematical models applicable to legged robots, and use that knowledge to strongly inform data-driven methods. We show that the existence of these simple structures can greatly facilitate robust design of legged robots from a data-driven perspective. We begin by demonstrating that the factorial complexity of hybrid models can be elegantly resolved with computationally tractable algorithms, and establish that a novel form of distributed control is predicted. We then continue by demonstrating that a relaxed version of the famous templates and anchors hypothesis can be used to encode performance objectives in a highly redundant way, allowing robots that have suffered damage to autonomously compensate. We conclude with a deadbeat stabilization result that is quite general, and can be determined without equations of motion.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155053/1/gcouncil_1.pd

Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2015

This volume contains the full papers accepted for presentation at the ECCOMAS Thematic Conference on Multibody Dynamics 2015 held in the Barcelona School of Industrial Engineering, Universitat Politècnica de Catalunya, on June 29 - July 2, 2015. The ECCOMAS Thematic Conference on Multibody Dynamics is an international meeting held once every two years in a European country. Continuing the very successful series of past conferences that have been organized in Lisbon (2003), Madrid (2005), Milan (2007), Warsaw (2009), Brussels (2011) and Zagreb (2013); this edition will once again serve as a meeting point for the international researchers, scientists and experts from academia, research laboratories and industry working in the area of multibody dynamics. Applications are related to many fields of contemporary engineering, such as vehicle and railway systems, aeronautical and space vehicles, robotic manipulators, mechatronic and autonomous systems, smart structures, biomechanical systems and nanotechnologies. The topics of the conference include, but are not restricted to: ● Formulations and Numerical Methods ● Efficient Methods and Real-Time Applications ● Flexible Multibody Dynamics ● Contact Dynamics and Constraints ● Multiphysics and Coupled Problems ● Control and Optimization ● Software Development and Computer Technology ● Aerospace and Maritime Applications ● Biomechanics ● Railroad Vehicle Dynamics ● Road Vehicle Dynamics ● Robotics ● Benchmark ProblemsPostprint (published version

Spacecraft/Rover Hybrids for the Exploration of Small Solar System Bodies

This study investigated a mission architecture that allows the systematic and affordable in-situ exploration of small solar system bodies, such as asteroids, comets, and Martian moons (Figure 1). The architecture relies on the novel concept of spacecraft/rover hybrids,which are surface mobility platforms capable of achieving large surface coverage (by attitude controlled hops, akin to spacecraft flight), fine mobility (by tumbling), and coarse instrument pointing (by changing orientation relative to the ground) in the low-gravity environments(micro-g to milli-g) of small bodies. The actuation of the hybrids relies on spinning three internal flywheels. Using a combination of torques, the three flywheel motors can produce a reaction torque in any orientation without additional moving parts. This mobility concept allows all subsystems to be packaged in one sealed enclosure and enables the platforms to be minimalistic. The hybrids would be deployed from a mother spacecraft, which would act as a communication relay to Earth and would aid the in-situ assets with tasks such as localization and navigation (Figure 1). The hybrids are expected to be more capable and affordable than wheeled or legged rovers, due to their multiple modes of mobility (both hopping and tumbling), and have simpler environmental sealing and thermal management (since all components are sealed in one enclosure, assuming non-deployable science instruments). In summary, this NIAC Phase II study has significantly increased the TRL (Technology Readiness Level) of the mobility and autonomy subsystems of spacecraft/rover hybrids, and characterized system engineering aspects in the context of a reference mission to Phobos. Future studies should focus on improving the robustness of the autonomy module and further refine system engineering aspects, in view of opportunities for technology infusion