Manipulability analysis of a snake robot without lateral constraint for head position control

Two dynamic manipulability criteria of a snake robot with sideways slipping are proposed with the application to head trajectory tracking control in mind. The singular posture, which is crucial in head tracking control, is characterized by the manipulability and examined for families of typical robot shapes. Differences in the singular postures from those of the robot with lateral constraints, which have not been clear in previous studies, are clarified in the analysis. In addition to the examination of local properties using the concept of manipulability, we discuss the effect of isotropic friction as a global property. It is well known that, at least empirically, a snake robot needs anisotropy in friction to move by serpentine locomotion if there are no objects for it to push around. From the point of view of integrability, we show one of the necessary conditions for uncontrollability is satisfied if the friction is isotropic

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

The Mechanics and Control of Undulatory Robotic Locomotion

In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle. We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations. The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations. The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields. The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets

Head-Trajectory-Tracking Control of a Snake Robot and Its Robustness Under Actuator Failure

This brief considers the problem of trajectory tracking of a planar snake robot without a lateral constraint. The reference trajectory of the head position and the orientation of link 1 are given, and torque control is determined to reduce tracking errors. The performance of the controller was tested in a number of simulations. The robustness during actuator failure was also studied. We assumed that one of the actuators was broken and the corresponding joint became passive. Furthermore, as a more realistic situation, we considered an instance when some of the states were not readily accessible from the sensor readings and needed to be estimated by an observer. The extended Kalman filter was employed for this purpose, and the performance of the closed-loop system with the observer was also tested in simulations

Stability analysis of snake robot locomotion based on Poincaré maps

Abstract — This paper presents an analysis of snake locomotion that explains how non-uniform viscous ground friction conditions enable snake robots to locomote forward on a planar surface. The explanation is based on a simple mapping from link velocities normal to the direction of motion into propulsive forces in the direction of motion. From this analysis, a controller for a snake robot is proposed. A Poincaré map is employed to prove that all state variables of the snake robot, except for the position in the forward direction, trace out an exponentially stable periodic orbit. I

Symmetries in Motion: Geometric Foundations of Motion Control

Some interesting aspects of motion and control, such as those found in biological and robotic locomotion and attitude control of spacecraft, involve geometric concepts. When an animal or a robot moves its joints in a periodic fashion, it can rotate or move forward. This observation leads to the general idea that when one variable in a system moves in a periodic fashion, motion of the Whole object can result. This property can be used for control purposes; the position and attitude Of a satellite, for example, are often controlled by periodic motions of parts of the satellite, such as spinning rotors. One of the geometric tools that has been used to describe this phenomenon is that of connections, a notion that is used extensively in general relativity and other parts of theoretical physics. This tool, part of the general subject Of geometric mechanics, has been helpful in the study of both the stability and instability of a system and system bifurcations, that is, changes in the nature of the system dynamics, as some parameter changes. Geometric mechanics, currently in a period of rapid evolution, has been used, for example, to design stabilizing feedback control systems in attitude dynamics. Theory is also being developed for systems with rolling constraints such as those found in a simple rolling wheel. This paper explains how some of these tools of geometric mechanics are used in the study of motion control and locomotion generation

MIRRAX: A Reconfigurable Robot for Limited Access Environments

The development of mobile robot platforms for inspection has gained traction in recent years with the rapid advancement in hardware and software. However, conventional mobile robots are unable to address the challenge of operating in extreme environments where the robot is required to traverse narrow gaps in highly cluttered areas with restricted access. This paper presents MIRRAX, a robot that has been designed to meet these challenges with the capability of re-configuring itself to both access restricted environments through narrow ports and navigate through tightly spaced obstacles. Controllers for the robot are detailed, along with an analysis on the controllability of the robot given the use of Mecanum wheels in a variable configuration. Characterisation on the robot's performance identified suitable configurations for operating in narrow environments. The minimum lateral footprint width achievable for stable configuration ($<2^\text{o}$~roll) was 0.19~m. Experimental validation of the robot's controllability shows good agreement with the theoretical analysis. A further series of experiments shows the feasibility of the robot in addressing the challenges above: the capability to reconfigure itself for restricted entry through ports as small as 150mm diameter, and navigating through cluttered environments. The paper also presents results from a deployment in a Magnox facility at the Sellafield nuclear site in the UK -- the first robot to ever do so, for remote inspection and mapping.Comment: 10 pages, Under review for IEEE Transactions on Robotic

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article