Abstract
This work develops a concept of singular configurations of non-holonomic systems, rooted in the endogenous configuration space approach. The approach takes as a starting point a control system representation of the equations of motion of a non-holonomic robotic system in the form of a control affine system with output. The input-output map is introduced whose derivative is defined as the system’s Jacobian. Dynamic singular configurations are defined as control functions at which the input-output map is not surjective, i.e. the system’s Jacobian gets rank deficient. It is shown that the dynamic singularities coincide with the singular optimal controls of the control affine system. As a by-product of the Jacobian setting dynamic dexterity measures of the non-holonomic systems are designed. The concept of dynamic singularities is illustrated with an example of the front wheel driven car.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abraham, R., Marsden, J.E., Ratiu, T.: Manifolds, Tensor Analysis, and Applications. Springer, New York (1988)
Chitour, Y., Sussmann, H.J.: Motion planning using the continuation method. Essays on Mathematical Robotics, pp. 91–125. Springer, New York (1988)
Chitour, Y., Jean, F., Trélat, E.: Singular trajectories of control-affine systems. SIAM J. Control Optim. 47, 1078–1095 (2008)
Kryński, W.: Singular curves determine generic distributions of corank at least 3. J. Dyn. Control Syst. 11, 375–388 (2005)
Montgomery, R.: A survey on singular curves in sub-Riemannian geometry. J. Dyn. Control Syst. 1, 49–90 (1995)
Müller, A.: A proposal for a unified concept of kinematic singularities for holonomic and non-holonomic mechanisms. In: Proceedings of the 36th Mech. Robotics Conference ASME 2012 International Design Engineering Technical Conferences, pp. 1543–1552. Chicago, IL (2012)
Müller, A., Donelan, P.: Towards a unified notion of kinematic singularities for robot arms and non-holonomic platforms (INRIA). Advances in Robot Kinematics, pp. 397–405. Springer, Berlin (2016)
Tchoń, K.: On kinematic singularities of nonholonomic robotic systems. In: Proceedings of RoManSy, vol. 13, pp. 75–84. Zakopane, Poland (2000)
Tchoń, K., Jakubiak, J.: Endogenous configuration space approach to mobile manipulators: a derivation and performance assessment of Jacobian inverse kinematics algorithms. Int. J. Control 76, 1387–1419 (2003)
Tchoń, K., Sienkiewicz, H.: Kinematic singularities of mobile manipulators: an analytic approach. Advances in Robot Kinematics, pp. 407–415. INRIA (2016)
Zadarnowska, K., Tchoń, K.: A control theory framework for performance evaluation of mobile manipulators. Robotica 25, 703–715 (2007)
Acknowledgements
This research was supported by the Wrocław University of Technology under a statutory research project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Tchoń, K. (2018). Dynamic Singularities of Non-holonomic Robotic Systems: An Analytic Approach. In: Lenarčič, J., Merlet, JP. (eds) Advances in Robot Kinematics 2016. Springer Proceedings in Advanced Robotics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-56802-7_42
Download citation
DOI: https://doi.org/10.1007/978-3-319-56802-7_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56801-0
Online ISBN: 978-3-319-56802-7
eBook Packages: EngineeringEngineering (R0)