The Soft Landing Problem: Minimizing Energy Loss by a Legged Robot Impacting Yielding Terrain

Enabling robots to walk and run on yielding terrain is increasingly vital to endeavors ranging from disaster response to extraterrestrial exploration. While dynamic legged locomotion on rigid ground is challenging enough, yielding terrain presents additional challenges such as permanent ground deformation which dissipates energy. In this paper, we examine the soft landing problem: given some impact momentum, bring the robot to rest while minimizing foot penetration depth. To gain insight into properties of penetration depth-minimizing control policies, we formulate a constrained optimal control problem and obtain a bang-bang open-loop force profile. Motivated by examples from biology and recent advances in legged robotics, we also examine impedance-control solutions to the dimensionless soft landing problem. Through simulations, we find that optimal impedance reduces penetration depth nearly as much as the open-loop force profile, while remaining robust to model uncertainty. Through simulations and experiments, we find that the solution space is rich, exhibiting qualitatively different relationships between impact velocity and the optimal impedance for small and large dimensionless impact velocities. Lastly, we discuss the relevance of this work to minimum-cost-of-transport locomotion for several actuator design choices

The separate neural control of hand movements and contact forces

To manipulate an object, we must simultaneously control the contact forces exerted on the object and the movements of our hand. Two alternative views for manipulation have been proposed: one in which motions and contact forces are represented and controlled by separate neural processes, and one in which motions and forces are controlled jointly, by a single process. To evaluate these alternatives, we designed three tasks in which subjects maintained a specified contact force while their hand was moved by a robotic manipulandum. The prescribed contact force and hand motions were selected in each task to induce the subject to attain one of three goals: (1) exerting a regulated contact force, (2) tracking the motion of the manipulandum, and (3) attaining both force and motion goals concurrently. By comparing subjects' performances in these three tasks, we found that behavior was captured by the summed actions of two independent control systems: one applying the desired force, and the other guiding the hand along the predicted path of the manipulandum. Furthermore, the application of transcranial magnetic stimulation impulses to the posterior parietal cortex selectively disrupted the control of motion but did not affect the regulation of static contact force. Together, these findings are consistent with the view that manipulation of objects is performed by independent brain control of hand motions and interaction forces

Robotic Contact Juggling

We define "robotic contact juggling" to be the purposeful control of the motion of a three-dimensional smooth object as it rolls freely on a motion-controlled robot manipulator, or "hand." While specific examples of robotic contact juggling have been studied before, in this paper we provide the first general formulation and solution method for the case of an arbitrary smooth object in single-point rolling contact on an arbitrary smooth hand. Our formulation splits the problem into four subproblems: (1) deriving the second-order rolling kinematics; (2) deriving the three-dimensional rolling dynamics; (3) planning rolling motions that satisfy the rolling dynamics; and (4) feedback stabilization of planned rolling trajectories. The theoretical results are demonstrated in simulation and experiment using feedback from a high-speed vision system.Comment: 16 pages, 14 figures. | Supplemental Video: https://youtu.be/QT55_Q1ePfg | Code: https://github.com/zackwoodruff/rolling_dynamic

Modulation of hexokinase association with mitochondria analyzed with quantitative three-dimensional confocal microscopy

Hexokinase isozyme I is proposed to be associated with mitochondria in vivo. Moreover, it has been suggested that this association is modulated in coordination with changes in cell metabolic state. To test these hypotheses, we analyzed the subcellular distribution of hexokinase relative to mitochondria in paraformaldehyde-fixed astrocytes using immunocytochemistry and quantitative three-dimensional confocal microscopy. Analysis of the extent of colocalization between hexokinase and mitochondria revealed that approximately 70% of cellular hexokinase is associated with mitochondria under basal metabolic conditions. In contrast to the immunocytochemical studies, between 15 to 40% of cellular hexokinase was found to be associated with mitochondria after fractionation of astrocyte cultures depending on the exact fractionation conditions. The discrepancy between fractionation studies and those based on imaging of distributions in fixed cells indicates the usefulness of using techniques that can evaluate the distributions of cytosolic enzymes in cells whose subcellular ultrastructure is not severely disrupted. To determine if hexokinase distribution is modulated in concert with changes in cell metabolism, the localization of hexokinase with mitochondria was evaluated after inhibition of glucose metabolism with 2-deoxyglucose. After incubation with 2-deoxyglucose there was an approximate 35% decrease in the amount of hexokinase associated with mitochondria. These findings support the hypothesis that hexokinase is bound to mitochondria in rat brain astrocytes in vivo, and that this association is sensitive to cell metabolic state

Efficient, Responsive, and Robust Hopping on Deformable Terrain

Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid substrates. In this study we focus on the ramifications of plastic terrain deformation on the hop-to-hop energy dynamics of a spring-legged monopedal hopping robot animated by a switched-compliance energy injection controller. From this deliberately simple robot-terrain model, we derive a hop-to-hop energy return map, and we use physical experiments and simulations to validate the hop-to-hop energy map for a real robot hopping on a real deformable substrate. The dynamical properties (fixed points, eigenvalues, basins of attraction) of this map provide insights into efficient, responsive, and robust locomotion on deformable terrain. Specifically, we identify constant-fixed-point surfaces in a controller parameter space that suggest it is possible to tune control parameters for efficiency or responsiveness while targeting a desired gait energy level. We also identify conditions under which fixed points of the energy map are globally stable, and we further characterize the basins of attraction of fixed points when these conditions are not satisfied. We conclude by discussing the implications of this hop-to-hop energy map for planning, control, and estimation for efficient, agile, and robust legged locomotion on deformable terrain.Comment: 17 pages, 13 figures, submitted to IEEE Transactions on Robotic