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 Human Walking to Bipedal Robot Locomotion: Reflex Inspired Compensation on Planned and Unplanned Downsteps

Humans are able to negotiate downstep behaviors -- both planned and unplanned -- with remarkable agility and ease. The goal of this paper is to systematically study the translation of this human behavior to bipedal walking robots, even if the morphology is inherently different. Concretely, we begin with human data wherein planned and unplanned downsteps are taken. We analyze this data from the perspective of reduced-order modeling of the human, encoding the center of mass (CoM) kinematics and contact forces, which allows for the translation of these behaviors into the corresponding reduced-order model of a bipedal robot. We embed the resulting behaviors into the full-order dynamics of a bipedal robot via nonlinear optimization-based controllers. The end result is the demonstration of planned and unplanned downsteps in simulation on an underactuated walking robot.Comment: 8 pages, 9 figure

On the role of stability in animal morphology and neural control

Mechanical stability is vital for the fitness and survival of animals and is a crucial aspect of robot design and control. Stability depends on multiple factors, including the body\u27s intrinsic mechanical response and feedback control. But feedback control is more fragile than the body\u27s innate mechanical response or open-loop control strategies because of sensory noise and time-delays in feedback. This thesis examines the overarching hypothesis that stability demands have played a crucial role in how animal form and function arise through natural selection and motor learning. In two examples, finger contact and overall body stability, we investigated the relationship between morphology, open-loop control, and stability. By studying the stability of the internal degrees of freedom of a finger when pushing on a hard surface, we find that stability limits the force that we can produce and is a dominant aspect of the neural control of the finger\u27s muscles. In our study on whole body lateral stability during locomotion in terrestrial animals, we find that the overall body aspect ratio has evolved to ensure passive lateral stability on the uneven terrain of natural environments. Precisely gripping an object with the fingertips is a hallmark of human hand dexterity. In Chapter 2, we show how human fingers are intrinsically prone to a buckling-type postural instability and how humans use careful neural orchestration of our muscles so that the elastic response of our muscles can suppress the intrinsic instability. In Chapter 3, we extend these findings further to examine the nature of neuromuscular variability and how the nervous system deals with the need for muscle-induced stability. We find that there is structure to neuromuscular variability so that most of the variability lies within the subspace that does not affect stability. Inspired by the open-loop stable control of our index fingers, in Chapter 4, we derive open-loop stability conditions for a general mechanical linkage with arbitrary joint torques subjected to holonomic constraints. The solution that we derive is physically realizable as cable-driven active mechanical linkages. With a user-prescribed cable layout, we pose the problem of actuating the system to maintain stability while subject to goals like energy minimization as a convex optimization problem. We are thus able to use efficient optimization methods available for convex problems and demonstrate numerical solutions in examples inspired by the finger. Chapter 5 presents a general formulation of the stability criteria for active mechanical linkages subject to Pfaffian holonomic and non-holonomic constraints. Active mechanical linkages subject to multiple constraints represent the mechanics of systems spanning many domains and length scales, such as limbs and digits in animals and robots, and elastic networks like actin meshes in microscopic systems. We show that a constrained mechanical linkage with regular stiffness and damping, and circulation-free feedback, can only destabilize by static buckling when subject to holonomic constraints. In contrast, the same mechanical linkage, subject to a non-holonomic constraint, such as a skate contact, can exhibit either static buckling or flutter instability. Chapter 6 moves away from neural control and studies the shape of animal bodies and their relationship to stability in locomotion. We investigate why small land animals tend to have a crouched or sprawled posture, whereas larger animals are generally more upright. We propose a new hypothesis that the scaling of body aspect ratio with size is driven by the scale-dependent unevenness of natural terrain. We show that the scaling law arising from the need for stability on rough natural terrain correctly predicts the frontal aspect ratio scaling law across 335 terrestrial vertebrates and invertebrates, spanning eight orders of magnitude in mass so that smaller animals have a wider aspect ratio. We also carry out statistical analyses that consider the phylogenetic relationship among the species in our dataset to show that the scaling is not due to gradual changes of the traits over time. Thus, stability demands on natural terrain may have driven the macroevolution of body aspect ratio across terrestrial animals. Interrogating unstable and marginally stable behaviors has helped us identify the morphological and control features that allow animals to perform robustly in noisy environments where perfect sensory feedback cannot be assumed. Although the thesis identifies the `what\u27 and `why,\u27 further studies are needed to understand `how\u27 mechanics and development intertwine to give rise to control and form in growing and adapting biological organisms

Model-Based Stability Analysis for Mobile Manipulators

Analisi della stabilità del movimento di un sistema composto da piattaforma mobile, sulla quale è stato montato un robot a 6 assi rotazionali. Per questo si sono calcolate le reazioni vincolari alla base del manipolatore attraverso l'implementazione dell'algoritmo di Newton-Euler, ed è stato fatto un lavoro di parameter estimation per stimare i parametri dinamici del manipolatore. Successivamente è stato applicato l'algoritmo Moment-Height Stability Measur

Wheeled Mobile Robots: State of the Art Overview and Kinematic Comparison Among Three Omnidirectional Locomotion Strategies

In the last decades, mobile robotics has become a very interesting research topic in the feld of robotics, mainly because of population ageing and the recent pandemic emergency caused by Covid-19. Against this context, the paper presents an overview on wheeled mobile robot (WMR), which have a central role in nowadays scenario. In particular, the paper describes the most commonly adopted locomotion strategies, perception systems, control architectures and navigation approaches. After having analyzed the state of the art, this paper focuses on the kinematics of three omnidirectional platforms: a four mecanum wheels robot (4WD), a three omni wheel platform (3WD) and a two swerve-drive system (2SWD). Through a dimensionless approach, these three platforms are compared to understand how their mobility is afected by the wheel speed limitations that are present in every practical application. This original comparison has not been already presented by the literature and it can be used to improve our understanding of the kinematics of these mobile robots and to guide the selection of the most appropriate locomotion system according to the specifc application

Support polygon in the hybrid legged-wheeled CENTAURO robot: modelling and control

Search for the robot capable to perform well in the real-world has sparked an interest in the hybrid locomotion systems. The hybrid legged-wheeled robots combine the advantages of the standard legged and wheeled platforms by switching between the quick and efficient wheeled motion on the flat grounds and the more versatile legged mobility on the unstructured terrains. With the locomotion flexibility offered by the hybrid mobility and appropriate control tools, these systems have high potential to excel in practical applications adapting effectively to real-world during locomanipuation operations. In contrary to their standard well-studied counterparts, kinematics of this newer type of robotic platforms has not been fully understood yet. This gap may lead to unexpected results when the standard locomotion methods are applied to hybrid legged-wheeled robots. To better understand mobility of the hybrid legged-wheeled robots, the model that describes the support polygon of a general hybrid legged-wheeled robot as a function of the wheel angular velocities without assumptions on the robot kinematics or wheel camber angle is proposed and analysed in this thesis. Based on the analysis of the developed support polygon model, a robust omnidirectional driving scheme has been designed. A continuous wheel motion is resolved through the Inverse Kinematics (IK) scheme, which generates robot motion compliant with the Non-Sliding Pure-Rolling (NSPR) condition. A higher-level scheme resolving a steering motion to comply with the non-holonomic constraint and to tackle the structural singularity is proposed. To improve the robot performance in presence to the unpredicted circumstances, the IK scheme has been enhanced with the introduction of a new reactive support polygon adaptation task. To this end, a novel quadratic programming task has been designed to push the system Support Polygon Vertices (SPVs) away from the robot Centre of Mass (CoM), while respecting the leg workspace limits. The proposed task has been expressed through the developed SPV model to account for the hardware limits. The omnidirectional driving and reactive control schemes have been verified in the simulation and hardware experiments. To that end, the simulator for the CENTAURO robot that models the actuation dynamics and the software framework for the locomotion research have been developed