This paper studies the mechanics of undulatory locomotion. This type of locomotion is generated by a coupling of internal shape changes to external nonholonomic constraints. Employing methods from geometric mechanics, we use the dynamic symmetries and kinematic constraints to develop a specialised form of the dynamic equations which govern undulatory systems. These equations are written in term...

The position/force control of mechanical systems subject to a set of Pfaffian constraints is addressed in this paper. A reduced order dynamical description of such nonholonomic mechanical systems, including the constraints, is developed. Some properties of the dynamic model are then exploited to facilitate the controller design. Based on theory of guaranteed stability of uncertain systems, a ro...

The motion of nonholonomic mobile manipulators (NMMs) is inherently constrained by joint limits, velocity self-collisions and singularities. Most planning algorithms consider some the aforementioned constraints, however, a unified framework to deal with all them lacking. This paper proposes solution for kinematic trajectory tracking redundant NMMs that include constraints needed practical imple...

The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ‘pitchfork’ type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, ar...

The paper develops discretization schemes for mechanical systems for integration and optimization purposes through a discrete geometric approach. We focus on systems with symmetries, controllable shape (internal variables), and nonholonomic constraints. Motivated by the abundance of important models from science and engineering with such properties, we propose numerical methods specifically des...

Thispapergives the general constrainedPoincaré equationsofmotion formechanical systems subjected to holonomic and/or nonholonomic constraints that may or may not satisfy d’Alembert’s principle at each instant of time. It also extends Gauss’s principle of least constraint to include quasi-accelerations when the constraints are ideal, thereby expanding the compass of thisprinciple considerably.Th...

This paper is concerned with planning the motion of mobile robots in formation, which means certain geometrical constraints are imposed on the relative positions and orientations of the robots throughout their travel. Specifically, a method of planning motion for formations of mobile robots with nonholonomic constraints is presented. The kinematic equations developed allow a certain class of fo...

This paper studies the mechanics of undulatory locomotion. This type of locomotion is generated by a coupling of internal shape changes to external nonholonomic constraints. Employing methods from geometric mechanics, we use the dynamic symmetries and kinematic constraints to develop a specialised form of the dynamic equations which govern undulatory systems. These equations are written in term...

Nonholonomic mechanical systems naturally occur when there are rolling constraints [4] or Lagrangian symmetries leading to momentum constraints [1]. Examples include kinematic wheeled vehicles, free floating satellites with appendages, and simplified models of biomimetic locomotion. This work considers the local motion planning problem for a specific class of nonholonomic systems— those whose c...

A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the p...