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 template, 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.

This paper presents a framework for planning the motion of an η -fingered robot hand to create an inertial load on a grasped object to achieve a desired in-grasp sliding motion. The model of the sliding dynamics is based on a soft-finger limit surface contact model at each fingertip. A motion planner is derived to automatically solve for the finger motions for a given initial and desired configuration of the object relative to the fingers. Iterative planning and execution are shown to reduce the errors that occur due to the modeling and trajectory tracking errors. The framework is applied to the problem of regrasping a laminar object held in a pinch grasp. We propose a limited surface model of the contact pressure distribution at each finger to predict the sliding directions. Experimental validations are shown, including iterative error reduction and repeatability of the experiment.

This paper explores the role of anisotropic friction properties in vibratory parts manipulation. We show that direction-dependent surface friction properties can be used in conjunction with a vibrating plate to help design friction-induced velocity fields on the surface of the plate. Theoretical, simulation, and experimental results are presented quantifying the anisotropic friction effects of textured surfaces such as micromachined silicon and fabrics.

Previously we modeled the undulatory subsurface locomotion of the sandfish lizard with a sand-swimming robot which displayed performance comparable to the organism. In this work we control the lift forces on the robot by varying its head shape and demonstrate that these granular forces predict the vertical motion of the robot. Inspired by the tapered head of the sandfish lizard, we drag a wedge shaped object horizontally and parallel to its lower face through a granular medium and show that by varying the angle of the upper leading surface of the wedge, α, the lift force can be varied from positive to negative. Testing the robot with these wedges as heads results in vertical motion in the same direction as the lift force in the drag experiments. As the robot moves forward, the force on its head normal to the body plane results in a net torque imbalance which pitches the robot causing it to rise or sink within the medium. Since repeatedly varying α for a wedge head to achieve a desired lift is impractical, we test robot heads that approximate a wedge head inclined at varying angles by changing the angle of the bottom and top surfaces of the wedge, and show that similar lift control is achieved. Our results provide principles for the construction of robots that will be able to follow arbitrary trajectories within complex substrates like sand, and also lend support to hypotheses that morphological adaptations of desert-dwelling organisms aid in their subsurface locomotion.

A position-dependent asymptotic velocity field describes the motion of point parts sliding with friction on the surface of a rigid oscillating plate. These fields can be used to perform manipulation tasks such as sensorless positioning of one or several parts simultaneously. This paper examines the set of fields F generated by periodic plate motions M that combine a single in-plane component and a single out-of-plane component that have square wave accelerations with 50% duty cycles, identical periods, and an arbitrary phase between them. By deconstructing the full map Π : M → F into three simpler maps, we expose the structure of F and its relationship to M. To illustrate, we focus on particular plate motions in M that generate fields well approximated by polynomial functions of position with degree n ≤ 2. Numerical simulations suggest that fields generated from plate motions with more than a single inplane and a single out-of-plane component (all with the same period and square wave accelerations) are well approximated by linear combinations of fields in F.

We show that the frictional forces arising from simultaneous small amplitude periodic translation and rotation of a rigid plate cause parts on the plate to converge to or diverge from a line coinciding with the rotation axis. The relative phase between the translation and rotation determines whether the parts are attracted to or repelled from the rotation axis. Assuming that both the translational and rotational accelerations of the plate are ldquobang-bangrdquo and have identical frequencies, we derive the resultant velocity fields for point parts on the plate. For many choices of phase the speed of the part is approximately proportional to its distance from the rotation axis. The strength of the velocity field can be controlled by modulating the amplitude of the translational acceleration, or modulating the relative phase between the translational and rotational acceleration profiles. We also determine the phases that maximize part speed towards and away from the rotation axis. These optimal phases not only maximize part speed but also generate velocity fields that are nearly independent of the coefficient of friction.

We describe a vibratory part transport mechanism that utilizes both static and dynamic friction to linearly transport parts in a horizontal direction. We derive a horizontal driving profile for the feeder surface that maximizes the steady-state velocity of parts on the surface subject to acceleration limits on the surface. Experiments verify the predicted transport behavior. We then derive the optimal feeding motion for a surface that can move in both the horizontal and vertical directions.

By vibrating a rigid plate with up to six degrees of freedom, we can create a large family of programmable frictional force fields acting on parts resting on the plate. These fields can be used for sensorless part orientation, uncertainty-reducing transport, and simultaneous manipulation of multiple parts. The principle is demonstrated by a plate rotating about an axis below the plate. Simple oscillatory rotation produces a squeeze field that attracts and aligns parts along a center line. This behavior is confirmed in experiment. Motivated by this experimental confirmation, we use a simulation to find plate motions that yield a number of other useful primitive force fields. By sequencing these force fields, we can create any force field that is a convex combination of the primitives.