We develop Hamilton–Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a geometric account of the Hamiltonization, identify necessary and sufficient conditions for Hamiltonization, and apply the conventional Hamilton–Jacobi theor...

We study a discrete analog of the Lagrange-d’Alembert principle of nonhonolomic mechanics and give conditions for it to define a map and to be reversible. In specific cases it can generate linearly implicit, semi-implicit, or implicit numerical integrators for nonholonomic systems which, in several examples, exhibit superior preservation of the dynamics. We also study discrete nonholonomic syst...

We extend the standard de nition of manipulability to the case of a nonholonomic mobile manipulator built from an n joint robotic arm and a nonholonomic mobile platform. The e ects of mounting the arm on a nonholonomic platform are shown through the analysis of the manipulability thus de ned. Applications of criteria inherited from manipulability considerations are given to justify design and t...

An optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems. The motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system. A cost function is introduced to incorporate the control energy and the final state errors. The control inputs are determined to minimize the cost functional. By using...

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define a...

This note considers the tracking problem of nonholonomic dynamic systems with unknown inertia parameters. A new controller is proposed relying on newly defined tracking errors and the passivity property of the nonholonomic dynamic system. The proposed controller ensures that the entire state of the system asymptotically tracks the desired trajectory. Simulation results show effectiveness of the...

We show that the Suslov nonholonomic rigid body problem studied in [10, 13, 26] can be regarded almost everywhere as a generalized Chaply-gin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifol...

We present a novel mechanical system, the “landfish,” which takes advantage of a combination of articulation and a nonholonomic constraint to exhibit fishlike locomotion. We apply geometric mechanics techniques to establish the equations of motion in terms of the system’s nonholonomic momentum and analyze the system’s equilibrium properties. Finally, we demonstrate its locomotion capabilities u...

We show that the Suslov nonholonomic rigid body problem studied in [10, 13, 26] can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifold...