JP2007301708A - Nonholonomic manipulator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve a problem wherein the control of an inferior driving manipulator is difficult and has few example of the practical application though various kinds of study is performed in expectation of the light weight and low cost, make advantage of the inferior driving manipulator and facilitate the control. <P>SOLUTION: A first link is fixed to a planetary gear carrier of a planetary gear unit, a second link is fixed to the ring gear, and a pantograph is composed by adding a third link and a fourth link to them. An actuator is provided on a sun gear rotary shaft. It is confirmed that a hand part can be moved in an arbitrary circle trajectory or a diameter trajectory having an arbitrary angle with a simple proportional control, though it is the inferior driving manipulator by this constitution. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The structure of underactuated manipulators using nonholonomic constraints.

  A planar manipulator that moves the hand portion at the tip of the manipulator to an arbitrary position within an allowable range of the two-dimensional plane generally requires two independent actuators. Here, when one actuator is used, it is called an underactuated manipulator, and various studies have been made with the expectation of light weight and low cost. However, it is difficult to control to bring an object to a predetermined position, and there are few practical examples.

Problems to be solved by the invention

  Various studies have been made on underactuated manipulators with the expectation of light weight and low cost, but they are difficult to control and few examples have been put to practical use. A construction method that makes use of the advantage of the underactuated manipulator and makes the control easy is a problem.

Means for solving the problem

As shown in FIG. 1, it has a planetary gear unit composed of a sun gear 1, a ring gear 2, a planetary gear, and its carrier 3. The first link 4 is fixed to the planetary gear carrier, and the second link 5 is fixed to the ring gear. The pantograph is constructed by adding a third link 6 and a fourth link 7 to them. Further, as shown in FIG. 3, the sun gear rotating shaft is provided with an actuator so as to have a function of actively rotating. A hand portion 8 is provided at the tip of the pantograph.
The single characteristics of the planetary gear unit are shown in FIG. When the rotation speed of the sun gear is ω ₁ , the rotation speed of the planetary gear carrier is ω ₂ , and the rotation speed of the ring gear is ω ₃ The following relational expression is obtained.

The coordinates and parameters of the manipulator are shown in FIG. The motor 9 directly drives the sun gear. In this way, mathematical expressions relating to the motion of the manipulator can be described as (1) to (8).
First, Lagrangian is as follows.

Formula 1

here,

Formula 2

Formula 3

Formula 4

Formula 5

Formula 6

The equation of motion is

Formula 7

Formula 8

Here, since the non-driven variable θ is included in the second derivative terms (inertia terms) of θ and θ _S in the equations (7) and (8), as shown in Non-Patent Document 1, this system is non- It is clear that it is a holonomic system, and in general, there is a possibility that the tip of the pantograph can be moved to an arbitrary position on the plane with one actuator.
Further, Equation (4) from r can be controlled directly by theta _S, because theta _S from the configuration can be controlled directly by the actuator torque T _S, r It can be seen that can be controlled by T _S. Then, Equation (7), when adding (8), theta 2-order differential term of _S from becoming only I _S, it can be seen that the theta is set smaller I _S can be controlled by T _S .
As described above, if both r and θ are independent controls, it can be predicted that the control to reach the target value can be performed with relatively simple control.
Non-Patent Document 1: G.A. Oriolo, Y. et al. Nakamura, Control of Mechanical System with Second-order Nonholonomic Constants: Underduced Manipulators, Proc. 30 ^th IEEE Int. Conf. On Decision and Control, 2398/2403 (1991)

The invention's effect

Next, the performance is confirmed by simulation. The simulation was performed with MATLAB / SIMULLINK. Considering the manipulator of the form shown in FIG. 1, the planetary gear shown in FIG. 2 is used, the parameters and variables are defined as shown in FIG. 3, and the simulation is performed using the models shown in equations (7) and (8). It was.
FIGS. 4 to 7 show the results of performing control to bring θ closer to 1.0 from the initial state r = 1.0 and θ = 0.0. The set parameters and control laws are also shown in FIG.
FIGS. 8 to 11 show the results of control to bring r close to 0.3 from the initial state r = 1.0 and θ = 0.0.
The set parameters and control laws are also shown in FIG.
In any case, it can be seen that the target is achieved only by simple proportional + differential control.
A general underactuated manipulator, for example, a rotating two-axis manipulator having two links placed in a horizontal plane, becomes a nonholonomic manipulator when the central axis is driven. However, the above control result was obtained by simple proportional control. There is no report, and it seems impossible with proportional control.

  FIG. 12 shows a comparison between driving one gear shaft with an actuator and driving a relative angle of two gear shafts. As a result, when driving one gear shaft, the inertia matrix includes the non-driving variable θ, so this system is a nonholonomic system, but when driving the relative angle of the two gear shafts, the inertia matrix contains Since the non-driving variable θ is not included, it can be seen that this system becomes a holonomic system and cannot be controlled by one actuator.

FIG. 13 shows an example in which the present invention is applied to an inspection support robot. In the figure, three workers are performing a final inspection of the product 11 from the assembly process on the work table 10 having a round table shape. Since the inspection of this product requires a high degree of skill, this is a case where a skilled worker must perform the inspection. After inspection, OK and NG products are separated and transported to the packing process or repair process.
The robot main body of the present invention is fixed to the center part or ceiling of the round table-like work table 10, and the movement range of the hand part at the tip of the pantograph covers the whole round table.
Here, the role of the robot is to carry the product 11 coming from the assembly process to the worker's place and to pass the completed product to the packaging process. In the figure, the worker 12 instructs the robot to carry the product, and the robot grasps the product 11 from the assembly process and carries it to the worker C. Since the control is such that r shown in FIG. 10 is made constant, the product is carried along the trajectory of the alternate long and short dash line in FIG. 13 while performing non-holonomic motion. Here, the operator 12 grasps the handle provided in the robot hand unit 8, pulls the robot hand forward, moves to a position where it can be easily operated, and then lowers the product onto the work table. In such a situation where the robot is controlling the product along a circular orbit, an interrupt operation in which a human interrupts and moves to the position he desires is difficult unless a nonholonomic mechanism is used. In the nonholonomic mechanism, r and θ are not directly controlled by a motor but are controlled through inertial force, so that an operator can move a product relatively freely in the r and θ directions.

  In this way, in collaborative work between humans and robots, by giving the function that the operator interrupts the controlled robot and gives priority to the operator's operation, the product can be freely lowered to a position where the worker can easily work. In addition, since the operator can flexibly determine the work position by his / her own intention, the environment of the worker is improved and the burden is reduced. In addition, when the worker 12 is a beginner, the worker must move the position of the 13 closer to 12 in order to show a model, or temporarily increase the operating rate of the line, as long as the space permits. Even when an operator has to be input, there is an advantage that a flexible response is possible by inputting the operator as shown by a dotted line in the figure without changing the control method of the manipulator.

  Furthermore, as shown in comparison with FIGS. 14 and 15, the nonholonomic manipulator basically moves so as to escape when an external force is applied to the hand part, so even if an operator accidentally hits the arm or face against the hand part Is small and difficult to be injured. For this reason, the effect of ensuring safety in human-robot cooperative work is also great. As shown in FIGS. 14A and 14B, the conventional two-dimensional manipulator damages the product and the obstacle because the motor torque is directly applied to the obstacle even if it hits the obstacle while rotating at a constant r. As shown in FIGS. 15 (a) and 15 (b), the two-dimensional manipulator according to the present invention has a constant r and the product moves in the r direction even if the motor torque or rotation speed does not change when it hits an obstacle while rotating Because it escapes, the motor torque is not directly applied to the obstacle and does not damage the product or the obstacle. 14 and 15, it is not necessary to consider the impact caused by the inertial force when the product to be transported hits an obstacle because the rotation speed of the manipulator is sufficiently small.

Although the above is an example applied to an inspection process, it can also be applied in an assembly process.
Moreover, the merit of the nonholonomic manipulator in the collaborative work of humans and robots can be utilized even in service industries such as restaurants and home care support.
When trying to do this with a conventional position control manipulator, it is necessary to release the transmission mechanism between the hand portion and the actuator with a one-end clutch, and the configuration becomes complicated. Therefore, it is difficult to realize it unless it is a nonholonomic manipulator.

BEST MODE FOR CARRYING OUT THE INVENTION

The best mode for carrying out the present invention will be described below with reference to the drawings.
The form is shown in FIG. The basic configuration is the same as in FIG. 1, but the hand portion and the planetary gear carrier portion 14 are set with a clearance in the vertical direction so that the hand portion and the carrier portion do not interfere even near r = 0. Can be moved to any position within the circle of r = 1.

  Since the tip of the manipulator can be moved on an arbitrary circular orbit or diameter line around the gear axis, if the operation of the hand part is linked well, a manipulator that is highly useful in handling paints and objects and supplying parts It becomes.

It is a general view of the manipulator of the present invention. It is explanatory drawing of a structure and characteristic of a planetary gear. It is explanatory drawing of a parameter, a variable, and a coordinate. The simulation result {circle over (1)} in the case where control is performed so that θ is constant. (Plane trajectory of hand part) The simulation result {circle over (2)} is obtained when the control is performed so that θ is constant. (Θ, its velocity, acceleration time waveform) The simulation result {circle over (3)} when the control is performed so that θ is constant. (R time waveform) The simulation result (4) in the case where control is performed so that θ is constant. (Time waveform of the control torque _{T S)} The simulation result {circle over (1)} in the case where control is performed so that r becomes constant. (Plane trajectory of hand part) A simulation result {circle over (2)} when control is performed so that r is constant. (Θ, its velocity, acceleration time waveform) A simulation result {circle over (3)} when control is performed so that r becomes constant. (R time waveform) Simulation result (4) in the case where control is performed so that r is constant. (Time waveform of the control torque _{T S)} It is a comparison figure of the characteristic difference by the difference in actuator arrangement. It is an Example at the time of applying this manipulator to inspection work. It is a figure which shows the state before the conventional manipulator hits an obstruction. It is a figure which shows the state when the conventional manipulator hits an obstacle. It is a figure which shows the state before the manipulator of this invention hits an obstruction. It is a figure which shows a state when the manipulator of this invention hits an obstruction. The best mode for carrying out is shown.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Sun gear 2 Ring gear 3 Planetary gear carrier 4 First link 5 Second link 6 Third link 7 Fourth link 8 Hand part 9 Motor 10 Round table work table 11 Product 12 Worker 13 Worker

Claims (5)

  It has a planetary gear unit consisting of a sun gear, a ring gear, and a planetary gear, and a first link is fixed to the sun gear, ring gear, or planetary gear carrier, and a second link is fixed to the remaining gear or carrier. Add three or four links to construct a pantograph. A manipulator characterized in that an actuator is provided on any one of the three kinds of gears or carriers to have a function of actively rotating.   The manipulator according to claim 1, wherein a hand unit having a function of holding an object is provided at a tip of the pantograph.   2. The manipulator according to claim 1, wherein a unit having a function of discharging fluid and adjusting the fluid is provided at a tip of the pantograph.   The polar coordinate of the tip of the pantograph is (r, cos θ) (where r is the length from the gear center axis to the pantograph tip, and θ is a straight line connecting the reference line passing through the gear center axis and the pantograph tip from the gear center axis. A manipulator that is controlled to draw an arbitrary r constant circular orbit.   A manipulator characterized by controlling so as to draw an arbitrary θ-constant linear trajectory when the polar coordinate at the tip of the pantograph is (r, cos θ).