Control of a Bicycle Using Virtual Holonomic Constraints

The paper studies the problem of making Getz's bicycle model traverse a strictly convex Jordan curve with bounded roll angle and bounded speed. The approach to solving this problem is based on the virtual holonomic constraint (VHC) method. Specifically, a VHC is enforced making the roll angle of the bicycle become a function of the bicycle's position along the curve. It is shown that the VHC can be automatically generated as a periodic solution of a scalar periodic differential equation, which we call virtual constraint generator. Finally, it is shown that if the curve is sufficiently long as compared to the height of the bicycle's centre of mass and its wheel base, then the enforcement of a suitable VHC makes the bicycle traverse the curve with a steady-state speed profile which is periodic and independent of initial conditions. An outcome of this work is a proof that the constrained dynamics of a Lagrangian control system subject to a VHC are generally not Lagrangian.Comment: 18 pages, 8 figure

On the Lagrangian Structure of Reduced Dynamics Under Virtual Holonomic Constraints

This paper investigates a class of Lagrangian control systems with $n$ degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which the reduced dynamics are those of a mechanical system with one DOF and, more generally, under which they have a Lagrangian structure. In both cases, we show that typical solutions satisfying the virtual constraints lie in a restricted class which we completely characterize.Comment: 23 pages, 5 figures, published online in ESAIM:COCV on April 28th, 201

Virtual Holonomic Constraints for Euler-Lagrange systems under sampling

In this paper, we consider the problem of imposing Virtual Holonomic Constraints to mechanical systems in Euler-Lagrangian form under sampling. An exact solution based on multi-rate sampling of order two over each input channel is described. The results are applied to orbital stabilization of the pendubot with illustrative simulations

Hybrid Virtual Holonomic Constraints for a 2-D.O.F. Bipedal Robot

Lawati, M. A., & Nielsen, C. (2015). Hybrid virtual holonomic constraints for a 2-D.O.F. bipedal robot. 2015 IEEE 28th Canadian Conference on Electrical and Computer Engineering (CCECE), 320–325. https://doi.org/10.1109/CCECE.2015.7129296We apply virtual holonomic constraints (VHCs) to a fully actuated Euler-Lagrange system with impacts : a bipedal walking robot consisting of a stance leg, swing leg and hip mass. We call these hybrid virtual holonomic constraints (hVHCs). For any desired gait of the bipedal robot, the angular position of the swing leg is expressed as a function of the angular position of the stance leg. Using this function, a hVHC is formed and the control objective is to constrain the dynamics of the robot to evolve on the constraint manifold. A design procedure is developed to generate feasible hVHCs for a 2-DOF bipedal robot. Simulation results are presented.Funder 1, This work was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) || Funder 2, by Sultan Qaboos University

Real-Time Planning with Primitives for Dynamic Walking over Uneven Terrain

We present an algorithm for receding-horizon motion planning using a finite family of motion primitives for underactuated dynamic walking over uneven terrain. The motion primitives are defined as virtual holonomic constraints, and the special structure of underactuated mechanical systems operating subject to virtual constraints is used to construct closed-form solutions and a special binary search tree that dramatically speed up motion planning. We propose a greedy depth-first search and discuss improvement using energy-based heuristics. The resulting algorithm can plan several footsteps ahead in a fraction of a second for both the compass-gait walker and a planar 7-Degree-of-freedom/five-link walker.Comment: Conference submissio

Formation Control of Underactuated Bio-inspired Snake Robots

This paper considers formation control of snake robots. In particular, based on a simplified locomotion model, and using the method of virtual holonomic constraints, we control the body shape of the robot to a desired gait pattern defined by some pre-specified constraint functions. These functions are dynamic in that they depend on the state variables of two compensators which are used to control the orientation and planar position of the robot, making this a dynamic maneuvering control strategy. Furthermore, using a formation control strategy we make the multi-agent system converge to and keep a desired geometric formation, and enforce the formation follow a desired straight line path with a given speed profile. Specifically, we use the proposed maneuvering controller to solve the formation control problem for a group of snake robots by synchronizing the commanded velocities of the robots. Simulation results are presented which illustrate the successful performance of the theoretical approach.© ISAROB 2016. This is the authors' accepted and refereed manuscript to the article. Locked until 2017-07-27