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We built a simple two-leg toy that can walk stably with no control system. It walks downhill powered only by gravity. It seems to be the first McGeer-like passive-dynamic walker that is statically unstable in all standing positions, yet is…
This paper provides new results for a tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid complexities and…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…
Soft robotic snakes made of compliant materials can continuously deform their bodies and, therefore, mimic the biological snakes' flexible and agile locomotion gaits better than their rigid-bodied counterparts. Without wheel support, to…
The speed of a ball rolling without skidding or spinning on a surface $S$ is the length of the velocity of its center. We show that if the speed depends only on $p\in S$, then $S$ has constant mean curvature; and, conversely, that if the…
This paper proposes a Lyapunov based approach to control the rotation of a flat disk spinning in the space without external forces. The motion of the disk is governed by the Euler's rotation equation for spinning objects. The control is…
Slow and accurate finger and limb movements are essential to daily activities, but their neural control and governing mechanics are relatively unexplored. We consider neuromechanical systems where slow movements are produced by neural…
This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…
The torque-free motion of rigid body in gravitational field is analyzed. The coin lands on a soft surface (such as the palm of the hand) that allows no bouncing. The model assumes the coin as a rigid body with constant angular momentum…
A mechanical system consisting of a rigid body and attached Kirchhoff plates under the action of three independent controls torques is considered. The equations of motion of such model are derived in the form of a system of coupled…
The musculoskeletal humanoid can move well under environmental contact thanks to its body softness. However, there are few studies that actively make use of the environment to rest its flexible musculoskeletal body. Also, its complex…
A global model is presented that can be used to study attitude maneuvers of a rigid spacecraft in a circular orbit about a large central body. The model includes gravity gradient effects that arise from the non-uniform gravity field and…
Nonsmooth phenomena, such as abrupt changes, impacts, and switching behaviors, frequently arise in real-world systems and present significant challenges for traditional optimal control methods, which typically assume smoothness and…
If one is given a rigid triangle in the plane or space, we show that the only motion possible, where each vertex of the triangle moves along a straight line, is given by a hypocycloid line drawer in the plane, and a natural extension in…
Today, electric scooter is a trendy personal mobility vehicle. The rising demand and opportunities attract ride-share services. A common problem of such services is abandoned e-scooters. An autonomous e-scooter capable of moving to the…
In this paper we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the…
The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest…
In this paper the exact analytical solution of the motion of a rigid body with arbitrary mass distribution is derived in the absence of forces or torques. The resulting expressions are cast into a form where the dependence of the motion on…
Sliding friction between two dry surfaces is reasonably described by the speed-independent Amonton-Coulomb friction force law. However, there are many situations where the frictional contact points between two surfaces are "active" and may…
Three-dimensional simulations with fully resolved hydrodynamics are performed to study the dynamics of a single squirmer under gravity, in order to clarify its motion in the vicinity of a flat plate. Different dynamics emerge for different…