A Motion-Planning Algorithm for the Rolling-Body Problem

François, Alouges; Chitour, Yacine; Long, Ruixing

doi:10.1109/tro.2010.2053733

Cited by 39 publications

(52 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This situation first occurs for Lie brackets of length 5. For instance, given the pair (3,2), one has both…”

Section: )mentioning

confidence: 99%

“…The continuation method of [39] and [10] belongs to the class of Newton-type methods. See [2] for the application of this method to the rolling-body problem. Proving its convergence amounts to show the global existence for the solution of a nonlinear differential equation, which relies on handling the abnormal extremals associated to the control system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A global steering method for nonholonomic systems

Chitour

Jean

Long

2013

Journal of Differential Equations

Self Cite

View full text Add to dashboard Cite

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in Jean et al. (2005) [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in Murray and Sastry (1993) [29] for chainedform systems.

show abstract

“…This situation first occurs for Lie brackets of length 5. For instance, given the pair (3,2), one has both…”

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A global steering method for nonholonomic systems

Chitour

Jean

Long

2013

Journal of Differential Equations

Self Cite

View full text Add to dashboard Cite

show abstract

“…Under such an actuation, provided that the ball is dynamically symmetric with respect to the plane axes, the spinning of the ball around the vertical axis is canceled out and the ball moves in the so-called pure rolling mode. As a result, motion planning for such a system can be conducted in kinematic formulation, and a number of motion planning algorithms have been developed so far [9]- [14]. In general, however, the existence of the pure rolling mode in a rolling system depends on the inertia distribution as well as on how the system is actuated.…”

Section: Introductionmentioning

confidence: 99%

“…For the kinematic model with pure rolling constraint, tracing geodesic lines on the sphere results in geodesic lines in the contact plane and vice versa, and many algorithms exploit this property explicitly [9], [12], [13] or implicitly as a part of a more general procedure [14]. However, if the rolling is constrained dynamically, this propertygeodesic-to-geodesic mapping-does not, in general, hold true [15].…”

Section: Introductionmentioning

confidence: 99%

A Motion Planning Strategy for a Spherical Rolling Robot Driven by Two Internal Rotors

2014

View full text Add to dashboard Cite

This paper deals with a motion planning problem for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The key feature of the problem is that it can be stated only in Manuscript , provided by the authors. It has two files showing motion of the spherical rolling robot in the simulation example in Section III. The file animation_k 2.5.mp4 corresponds to the set of parameters k = 2.5 and η = 0.6. The file animation_k2.5.mp4 corresponds to the set of parameters k = 10 and η = 0.5. Its size is 20.6 Mb.Color versions of one or more of the figures in this paper are available online at dynamic formulation. In addition, the problem features a singularity when the contact trajectory goes along the equatorial line in the plane of the two rotors. A motion planning strategy composed of two trivial and one nontrivial maneuver is devised. The trivial maneuvers implement motion along the geodesic line perpendicular to the singularity line. The construction of the nontrivial maneuver employs the nilpotent approximation of the originally nonnilpotent robot dynamics, and is based on an iterative steering algorithm. At each iteration, the control inputs are constructed with the use of geometric phases. The motion planning strategy thus constructed is verified under simulation.

show abstract

“…The geometric approach yields an elegant and efficient way to treat optimal control problems, especially when applied to rolling bodies, e.g. see [43,44,45,46] and subsequent application of geometric theory to the trajectory planning of bodies rolling with and without twisting at the contact point [47]. In particular, the celebrated paper of Jurdjevic [43] demonstrates the analytical solution of the equations for the kinematically controlled ball rolling between two plates using the description of the rolling ball in terms of the Lie group SO(3) × R 2 .…”

Section: Equations Of Motion In Intrinsic Coordinatesmentioning

confidence: 99%

On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

Putkaradze

Rogers

2020

Journal of Dynamic Systems, Measurement, and Control

View full text Add to dashboard Cite

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. Application of the variational Pontryagin's minimum principle yields the ball's controlled equations of motion, a solution of which obeys the ball's uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index.

show abstract

A Motion-Planning Algorithm for the Rolling-Body Problem

Cited by 39 publications

References 19 publications

A global steering method for nonholonomic systems

A global steering method for nonholonomic systems

A Motion Planning Strategy for a Spherical Rolling Robot Driven by Two Internal Rotors

On the Optimal Control of a Rolling Ball Robot Actuated by Internal Point Masses

Contact Info

Product

Resources

About