HYBRID DYNAMICS IN MECHANICAL SYSTEMS

Mechanical Engineering

About this course

The course deals with dynamics of mechanical and robotic systems under constraints, and specifically kinematic constraints of contact with friction. Motion of such systems is typically described by a hybrid dynamical system with non-smooth solutions due to transitions between different contact states and impact at the contacts. These systems are useful for motion analysis and control design of robotic systems for object grasping and manipulation, as well as legged mobile robots and wheeled or tracked vehicles. The class discusses basic topics in addition to phenomena which are unique to hybrid systems, as well as advanced research problems. The course involves four homework assignments and a final project, all involving analysis and numerical computation in Matlab

Topics: Lagrange’s equations, formulating the dynamics of mechanical systems with holonomic and non-holonomic constraints, with mechanical and/or kinematic inputs. Contact kinematics and contact forces. Friction, Coulomb’s model, planar multi-contact statics – graphical and computational analysis. Dynamics under different contact states, Painlevé paradox and dynamic jamming. Impact models with and without friction, Zeno phenomenon, simple models of dynamic walking, Poincaré map, stability of periodic orbits in hybrid systems.

Text Books: (some are available in electronic format online or via Technion’s library)

1. M. T. Mason, "Mechanics of robotic manipulation", MIT Press 2001 LINK to Mason’s class lecture notes at CMU
2. R. M. Murray, Z. Li, S. Sastry, "Mathematical Introduction to Robotic manipulation", CRC press 1994. LINK to author’s online printout.
3. B. Brogliato, “Nonsmooth Mechanics: models, dynamics, and control”, Springer 1999
4. E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. H. Choi, and B. Morris, "Feedback Control of Dynamic Bipedal Robot Locomotion", CRC Press 2007

Expected learning outcomes

The class discusses basic topics in addition to phenomena which are unique to hybrid systems, as well as advanced research problems.

Semester Start Date: November 30, 2024

Contact Hours: 3

Day & Time: TBD