Frequency-Aware Model Predictive Control

Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance

In silico case studies of compliant robots: AMARSI deliverable 3.3

In the deliverable 3.2 we presented how the morphological computing ap- proach can significantly facilitate the control strategy in several scenarios, e.g. quadruped locomotion, bipedal locomotion and reaching. In particular, the Kitty experimental platform is an example of the use of morphological computation to allow quadruped locomotion. In this deliverable we continue with the simulation studies on the application of the different morphological computation strategies to control a robotic system

Active mechanics reveal molecular-scale force kinetics in living oocytes

Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in-vitro by single molecule approaches, however, their in-vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power-stroke, and velocity) of the in-vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration $\tau \sim$ 300 $\mu$s resulting in an average force of $F \sim$ 0.4 pN on vesicles in in-vivo oocytes, remarkably similar to the kinetics of in-vitro myosin-V. Our results reveal that measuring in-vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics.Comment: 20 pages, 4 figures, see ancillary files for Supplementary Materials, * equally contributing author

THE EFFECT OF JOINT MOBILIZATION ON FUNCTIONAL OUTCOMES ASSOCIATED WITH CHRONIC ANKLE INSTABILITY

Ankle sprains are among the most common injuries sustained by physically active individuals. Although ankle sprains are often considered innocuous in nature, a large percentage of individuals experience repetitive sprains, residual symptoms, and recurrent ankle instability following a single acute sprain; otherwise known as chronic ankle instability (CAI). In addition to repetitive ankle trauma, those with CAI experience reductions in functional capacity over the life span. This indicates that current intervention strategies for CAI are inadequate and require further investigation. The objective of this dissertation was to explore differences in walking and running gait parameters between individuals with and without CAI; as well as, examine the effects of a 2-week Maitland Grade III anterior-to-posterior talocrural joint mobilization intervention on self-reported function, ankle mechanics, postural control, and walking and running gait parameters in a cohort of individuals with CAI. It was hypothesized that individuals with CAI would exhibit different gait kinematics and joint coupling variability patterns compared to healthy individuals and the joint mobilization intervention would improve patient-oriented, clinician-oriented, and laboratory-oriented measures of function in those with CAI. Several observations were made from the results. In the first study, alterations in single joint kinematics and joint coupling variability were found between those with CAI and healthy individuals. In the second study, it was determined that the joint mobilization intervention improved patient-oriented and clinician-oriented measures of function as indicated by improved Foot and Ankle Ability Measure scores, increased weight-bearing dorsiflexion range of motion, and increased reach distances on the Star Excursion Balance Test. However, there were no changes in measures of instrumented ankle arthrometry or laboratory measures of postural control. In the third study, there were no changes in single joint kinematics or joint coupling variability during walking and running associated with the joint mobilization intervention. It can be concluded that joint mobilizations had a significant positive impact on patient-, and clinician-oriented measures of function. Though the laboratory measures did not detect any improvements, joint mobilizations did not produce deleterious effects on function. Therefore, future investigation on the effects of joint mobilization in conjunction with other, more active, rehabilitation strategies is warranted

The effects of muscle tissue mass on contractile performance

Skeletal muscles are the motors that drive human and animal locomotion. Yet despite their fundamental importance, our understanding of whole muscle behaviour is relatively limited due to practical and ethical considerations that hinder accurate in vivo measures. To estimate the behaviour of whole muscles, measures of single fibres or fibre bundles are often extrapolated to larger sizes without considering the consequences of the greater muscle mass. The goal of this thesis was to determine the effects of muscle mass on the contractile performance of whole skeletal muscles. In my first study, I developed a novel modelling framework to test different Hill-type model formulations under a range of cyclic contractile conditions. I then used this framework in my second study to examine the effects of distributed muscle mass on mass-specific mechanical work per cycle during cyclic contractions. I found that when the mass-enhanced muscle model was geometrically scaled from the size of a fibre bundle up to a whole human plantarflexor muscle, the mass-specific work per cycle decreased. In my third study, I examined the effects of muscle mass on the contractile behaviour of in situ rat plantaris muscle to validate the mass-enhanced Hill-type muscle model in my second study. In the fourth study of my thesis, I simulated cyclic contractions of a 3D continuum muscle model that accounts for tissue mass across a range of muscle sizes. I additionally compared the effects of greater muscle mass on tissue accelerations of the 3D muscle model to that of the in situ rat plantaris muscle from my third study to qualitatively validate the model simulations. I found that increasing the mass of the 3D muscle increased its volume-specific kinetic energy and was associated with lower mass-specific mechanical work per cycle. In my fifth study, I examined the effects of muscle mass on the metabolic cost and efficiency of muscle during cyclic contractions and how tendons of different stiffnesses alter these relationships. I found that larger muscles with greater mass are less efficient, primarily due to lower mass-specific mechanical work, and that the work and efficiency penalty of larger muscles can be offset to a certain extent by a tendon of optimal stiffness. Taken together, the results of these studies highlight that muscle mass is an important determinant of whole skeletal muscle behaviour

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

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