1) Design and Control of Underactuated Manipulators using Nonholonomic Constraints


   Figure 1: The Nonholonomic Manipulator                    Figure 2: The Nonholonomic Gear


      Figure 3: The Chained Form Manipulator.

The focus of this research is the definitions and developments of new nonholonomic machines which are designed on the basis of nonlinear control theory for nonholonomic mechanical systems. The start point of this study is to explore the possibility of innovative and useful mechanisms from the nonlinear control theoretic background.

Nonholonomic systems are typically controllable in a configuration space of higher dimension than that of the input space. The particular goal of this study is design and control of a manipulator consisting of n revolute joints using only two actuators, exploiting the unique feature of nonholonomic systems. A fabricated prototype of the nonholonomic manipulator is shown in figure 1. In order to create nonlinear kinematic structure, a nonholonomic gear was designed as a velocity transmission mechanism. The nonholonomic gear is composed of a ball and wheels and it can be used as a SIMO CVT (Single Input, Multiple Output, Continuously Variable Transmission). Figure 2 shows the nonholonomic gear, where rolling contact provides nonholonomic constraints.

Since the kinematic model of the nonholonomic manipulator is highly nonlinear, it was converted to the chained form, which is one of the canonical form of a class of nonlinear systems. Efficient motion planning and feedback control schemes were developed and successfully tested on the prototype.

Major research issues of the nonholonomic manipulator were 1) Theoretical design 2) Proof of controllability based on the Lie Algebra Lank Condition 3) Chained form conversion of the nonlinear kinematic model. 4) Mechanical design and implementation 5) Motion control using various open and closed loop control strategies.

There are possible alternative designs of the nonholonomic underactuated manipulator. The nonholonomic manipulator was designed focusing on the mechanical simplicity. The chained form manipulator was newly designed in order to achieve mathematically well-conditioned kinematic model. Figure 3 shows the prototype of the chained form manipulator.

A practical motion planning scheme was developed focusing on the initial condition sensitivity. This idea provided a resultant motion which is less sensitive to initial condition errors and disturbances, when the open loop control is carried out.

Research issues of the chained form manipulator were 1) Clarification of the mathematical problems of the nonlinear kinematic model 2) Design of the mechanical structure 3) Motion planning to minimize the initial condition sensitivity 4) Experimental verification of design and control schemes.

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