Tree-Structured Stick Breaking Processes for Hierarchical Data

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeable. One can view our model as providing infinite mixtures where the components have a dependency structure corresponding to an evolutionary diffusion down a tree. By using a stick-breaking approach, we can apply Markov chain Monte Carlo methods based on slice sampling to perform Bayesian inference and simulate from the posterior distribution on trees. We apply our method to hierarchical clustering of images and topic modeling of text data.

Functionally different pads on the same foot allow control of attachment: stick insects have load-sensitive "heel" pads for friction and shear-sensitive "toe" pads for adhesion.

Stick insects (Carausius morosus) have two distinct types of attachment pad per leg, tarsal "heel" pads (euplantulae) and a pre-tarsal "toe" pad (arolium). Here we show that these two pad types are specialised for fundamentally different functions. When standing upright, stick insects rested on their proximal euplantulae, while arolia were the only pads in surface contact when hanging upside down. Single-pad force measurements showed that the adhesion of euplantulae was extremely small, but friction forces strongly increased with normal load and coefficients of friction were [Formula: see text] 1. The pre-tarsal arolium, in contrast, generated adhesion that strongly increased with pulling forces, allowing adhesion to be activated and deactivated by shear forces, which can be produced actively, or passively as a result of the insects' sprawled posture. The shear-sensitivity of the arolium was present even when corrected for contact area, and was independent of normal preloads covering nearly an order of magnitude. Attachment of both heel and toe pads is thus activated partly by the forces that arise passively in the situations in which they are used by the insects, ensuring safe attachment. Our results suggest that stick insect euplantulae are specialised "friction pads" that produce traction when pressed against the substrate, while arolia are "true" adhesive pads that stick to the substrate when activated by pulling forces.

Surface contact and design of fibrillar 'friction pads' in stick insects (Carausius morosus): mechanisms for large friction coefficients and negligible adhesion.

Many stick insects and mantophasmids possess tarsal 'heel pads' (euplantulae) covered by arrays of conical, micrometre-sized hairs (acanthae). These pads are used mainly under compression; they respond to load with increasing shear resistance, and show negligible adhesion. Reflected-light microscopy in stick insects (Carausius morosus) revealed that the contact area of 'heel pads' changes with normal load on three hierarchical levels. First, loading brought larger areas of the convex pads into contact. Second, loading increased the density of acanthae in contact. Third, higher loads changed the shape of individual hair contacts gradually from circular (tip contact) to elongated (side contact). The resulting increase in real contact area can explain the load dependence of friction, indicating a constant shear stress between acanthae and substrate. As the euplantula contact area is negligible for small loads (similar to hard materials), but increases sharply with load (resembling soft materials), these pads show high friction coefficients despite little adhesion. This property appears essential for the pads' use in locomotion. Several morphological characteristics of hairy friction pads are in apparent contrast to hairy pads used for adhesion, highlighting key adaptations for both pad types. Our results are relevant for the design of fibrillar structures with high friction coefficients but small adhesion.

Bipedal walking and running with spring-like biarticular muscles.

Compliant elements in the leg musculoskeletal system appear to be important not only for running but also for walking in human locomotion as shown in the energetics and kinematics studies of spring-mass model. While the spring-mass model assumes a whole leg as a linear spring, it is still not clear how the compliant elements of muscle-tendon systems behave in a human-like segmented leg structure. This study presents a minimalistic model of compliant leg structure that exploits dynamics of biarticular tension springs. In the proposed bipedal model, each leg consists of three leg segments with passive knee and ankle joints that are constrained by four linear tension springs. We found that biarticular arrangements of the springs that correspond to rectus femoris, biceps femoris and gastrocnemius in human legs provide self-stabilizing characteristics for both walking and running gaits. Through the experiments in simulation and a real-world robotic platform, we show how behavioral characteristics of the proposed model agree with basic patterns of human locomotion including joint kinematics and ground reaction force, which could not be explained in the previous models.

Stable dynamic walking over uneven terrain

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated "dynamic walking" biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents "transversal" dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems. © The Author(s) 2011.