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The trajectories of a rational motion given by a polynomial of degree n in the dual quaternion model of rigid body displacements are generically of degree 2n. In this article we study those exceptional motions whose trajectory degree is…
A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot…
Legged locomotion is commonly studied and expressed as a discrete set of gait patterns, like walk, trot, gallop, which are usually treated as given and pre-programmed in legged robots for efficient locomotion at different speeds. However,…
Perching on {the surface} of moving objects, like vehicles, could extend the flight {time} and range of quadrotors. Suction cups are usually adopted for {surface attachment} due to their durability and large adhesive force. To seal on {a…
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 two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
We present a solvable biped walking model based on an inverted pendulum with two massless articulated legs capable of walking on uneven floors and inclined planes. The stride of the two-legged robot results from the pendular motion of a…
For the four-color theorem that has been developed over one and half centuries, all people believe it right but without complete proof convincing all1-3. Former proofs are to find the basic four-colorable patterns on a planar graph to…
Doppler radar systems enable unobtrusive and privacy-preserving long-term monitoring of human motions indoors. In particular, a person's gait can provide important information about their state of health. Utilizing micro-Doppler signatures,…
In this paper we present a class of four-dimensional bi-rational maps with two invariants satisfying certain constraints on degrees. We discuss the integrability properties of these maps from the point of view of degree growth and Liouville…
Gaits engineered for snake-like robots to rotate in-place instrumentally fill a gap in the set of locomotive gaits that have traditionally prioritized translation. This paper designs a Turn-in-Place gait and demonstrates the ability of a…
Get-Up-and-Go Test is commonly used for assessing the physical mobility of the elderly by physicians. This paper presents a method for automatic analysis and classification of human gait in the Get-Up-and-Go Test using a Microsoft Kinect…
We present a novel generative model, called Bidirectional GaitNet, that learns the relationship between human anatomy and its gait. The simulation model of human anatomy is a comprehensive, full-body, simulation-ready, musculoskeletal model…
This paper addresses the problem of designing a trajectory tracking control law for a quadrotor UAV, subsequent to complete failure of a single rotor. The control design problem considers the reduced state space which excludes the angular…
Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations…
Weingarten surfaces are those whose principal curvatures satisfy a functional relation, whose set of solutions is called the curvature diagram or the W-diagram of the surface. Making use of the notion of geometric linear momentum of a plane…
Characterizing what types of exoskeleton gaits are comfortable for users, and understanding the science of walking more generally, require recovering a user's utility landscape. Learning these landscapes is challenging, as walking…
Gait recognition is an appealing biometric modality which aims to identify individuals based on the way they walk. Deep learning has reshaped the research landscape in this area since 2015 through the ability to automatically learn…
Quadrupedal locomotion over complex terrain has been a long-standing research topic in robotics. While recent reinforcement learning-based locomotion methods improve generalizability and foot-placement precision, they rely on implicit…
In the author's earlier work there appeared a new way to specify any smooth closed 4-manifold by a surface diagram, which consists of an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each…