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Nonholonomic Behavior in Robotic Systems
Published in Richard M. Murray, Zexiang Li, S. Shankar Sastry, A Mathematical Introduction to Robotic Manipulation, 2017
Richard M. Murray, Zexiang Li, S. Shankar Sastry
Both this chapter and Chapter 8 are slightly more advanced in flavor than the previous chapters and represent some of the recent research in the robotics literature. Nonholonomic behavior also plays a strong role in many problems in geometric mechanics, which we touch on only briefly in the examples and exercises. In classical mechanics, nonholonomic behavior is closely related to the geometric phase associated with a group symmetry in a Hamiltonian or Lagrangian system. A good introduction to these concepts can be found in the lecture notes by Marsden [68].
6-DOF consensus control of multi-agent rigid body systems using rotation matrices
Published in International Journal of Control, 2022
Mohammad Maadani, Eric A. Butcher
The remainder of this paper is organised as follows. Some preliminaries on graph theory and geometric mechanics are given in Section 2. The consensus problems for attitude and 6-DOF dynamics of N heterogeneous rigid bodies are discussed in Section 3. The Lyapunov-based stability analysis with LaSalle's theorem are exploited to prove the stability of the consensus subspace of the closed-loop system for each of the two cases. The discretised variational integration method used in this paper is discussed in Section 4. Numerical simulations on consensus control of four rigid bodies are demonstrated in Section 5. Also, the presence of unstable non-consensus equilibria in the closed-loop dynamics is demonstrated through illustrative examples. Finally, the concluding remarks are provided in Section 6.
Perspectives on geometric numerical integration
Published in Journal of the Royal Society of New Zealand, 2019
A diagram from Book I, Theorem I of Newton's Principia is shown in Figure 1. It proves that a body moving under a central force sweeps out equal areas in equal times, or, in modern terms, the conservation of angular momentum for motion in a central force field. Since 1918 this property has been understood as an example of Noether's theorem, a cornerstone result in geometric mechanics. Newton has discretised the smooth motion of the planet into a repeated sequence of two steps (‘For suppose the time to be divided into equal parts’.). In the first step (AB), the planet moves in a straight line. In the second step, the planet does not move, but its velocity vector is changed under the influence of the central force from Bc to BC. The triangles SAB and SBC have the same area. He then lets the step size tend to zero (‘Now let the number of those triangles be augmented … ad infinitum’), arriving at the desired result for the continuous system.
Haptic tele-driving of wheeled mobile robot over the internet via PSPM approach: theory and experiment
Published in Advanced Robotics, 2018
Hyunsoo Yang, Zhiyuan Zuo, Dongjun Lee
Dongjun Lee(S’02-M’04) is an associate professor with the Department of Mechanical & Aerospace Engineering at the Seoul National University. He received the BS and MS degrees from KAIST, Korea, and the PhD degree in mechanical engineering from the University of Minnesota, respectively in 1995, 1997 and 2004. His main research interests are dynamics and control of robotic and mechatronic systems with emphasis on aerial robotics and manipulation, teleoperation/haptics, multirobot systems and geometric mechanics control theory. Dr Lee received the US NSF CAREER Award in 2009, the Best Paper Award from the IAS-2012, the Best Video Award from the URAI 2015, and the 2002–2003 Doctoral Dissertation Fellowship of the University of Minnesota. He was an Associate Editor of the IEEE Transactions on Robotics, and an Editor for the IEEE International Conference on Robotics & Automation 2015–2017.