JP2003011075A - Gravity center velocity control method for leg type moving machine - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a gravity center velocity control method highly speedily and precisely finding the sensitivity of the gravity center velocity relative to a whole joint angular velocity necessary for highly precisely operating the gravity center velocity of the leg type moving machine, or a complicated freedom degree nonlinear system. SOLUTION: A relative position and attitude of a link (ground link) stationary to environment at present out of constitution links to a basal link and a relative position of the gravity center to the basal link are found using a model including geometric information such as relative positional relations between respective links of the leg type moving machine and dynamic information such as positions of the gravity centers of the respective links. A sensitivity matrix of the gravity center velocity relative to the respective joint angular velocity is strictly calculated based thereon.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to velocity control of the center of gravity of a legged mobile machine.

[0002]

2. Description of the Related Art A machine having a multi-leg mechanism composed of rigid multi-links connected to a base link (hereinafter referred to as a legged mobile machine) does not have a fixed point on the ground, and therefore continues to operate while avoiding a fall. Balance maintenance control for that purpose is essential. Such balance control is performed by instantaneously manipulating the velocity of the center of gravity of the whole body, and as the agility of the motion increases, higher manipulation accuracy is required. However, legged mobile machines are generally complicated nonlinear systems with multiple degrees of freedom, and it is extremely difficult to control the center-of-gravity velocity with high accuracy. As a method of controlling the center-of-gravity velocity of a legged mobile machine, which is such a difficult problem, conventionally, the method of approximating only the center-of-gravity motion of the base link without ignoring the mass of the leg (Technical Report of the Institute of Mechanical Engineering, METI) 171,199
6), using neural networks (Proceedings of the 6th Annual Conference of the Robotics Society of Japan, pp.117-118, 1988),
Approximately obtaining the sensitivity to each joint angular velocity by numerical difference (Journal of the Robotics Society of Japan, Vol.17, No.2, pp.268-27)
4, 1999) was used, but all had problems in terms of accuracy, versatility, and calculation amount.

[0003]

The problem to be solved is required for operating the center of gravity speed of a general legged mobile machine, which is a complex multi-degree-of-freedom nonlinear system as described above, with high accuracy. It is to obtain the sensitivity of the center-of-gravity velocity to the total joint angular velocity at high speed and with high accuracy.

[0004]

In order to solve the above problems, according to the present invention, geometric information such as a relative positional relationship between each link of a legged mobile machine, and a position of a center of gravity of each link, etc. A model that contains the mechanical information of
Of the links that make up the legged mobile machine, the relative position and orientation of the link that is currently stationary with respect to the environment (such as the toe link of the supporting leg. Also, the relative position of the center of gravity to the base link is obtained, and the sensitivity of the center of gravity velocity to each joint angular velocity is calculated strictly based on them.

[0005]

According to the present invention, it becomes possible to express a strict relationship between the center-of-gravity velocity and each joint angular velocity of a legged mobile machine, which is a complex multi-degree-of-freedom nonlinear system, by a simple simultaneous linear equation. Based on this, a weighted generalized inverse matrix is used to calculate the appropriate target control amount for all joint angular velocities, and each joint is controlled so as to follow the target control amount. It becomes possible to obtain the joint angle operation amount for accurate operation at high speed. Also, if various constraint conditions other than the center-of-gravity velocity are added at the same time by being expressed as simultaneous equations, such as maintaining the velocity of the tip of the toe of the swing leg or the angular momentum around the center of gravity of the whole body at the specified values, summarize them when they are added simultaneously. By using the same solution method as one simultaneous equation, it becomes possible to operate the center-of-gravity velocity with high accuracy while satisfying the constraint condition. Furthermore, the present invention can be applied to general legged mobile machines without being limited to a specific mechanism, and has sufficient versatility and practicality.

[0006]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below by taking a general multi-legged robot as a legged mobile machine as an example. In addition,
For the purpose of explanation, a coordinate system fixed to the inertial system (hereinafter referred to as an absolute coordinate system), a coordinate system fixed to the robot base link (hereinafter referred to as a whole body coordinate system), and each link The coordinate system fixed to (hereinafter, referred to as a link coordinate system) is used separately. Especially in the link coordinate system, a link that is stably grounded on the ground (such as a toe link of a supporting leg)
The coordinate system fixed at is called the touchdown coordinate system. The relationship between the structure of a general multi-legged robot and the absolute coordinate system, whole body coordinate system, and ground coordinate system

Shown in Figure 1

In the following, n is the total number of degrees of freedom of the robot, θ is the total joint angle vector of the robot (n × 1 vector)
Is. If a stable grounding state of the system is secured, the center of gravity xG is a function of θ. At this time JG = ∂xG
/ ∂θ matrix (3 × n matrix) exists and
If G and the joint angular velocity are ω, the following equation holds.

[Equation 1] This JG is a matrix (hereinafter referred to as the whole body center of gravity Jacobian) that represents the sensitivity of the center of gravity velocity to each joint angular velocity.

JG is obtained as follows. First, the Jacobian 0JGi regarding the relative translational velocity viewed from the whole body coordinate system of the center of gravity of the i-th link is obtained for all links. For this purpose, for example, the method described in the document “Basics of Robotics (Haruhisa Kawasaki, Morikita Publishing, 1991)” and the like may be used.
Using these and each link mass mi, Jacobian 0JG regarding the velocity of the center of gravity in the whole body coordinate system is obtained from the following equation.

[Equation 2] If the Fth link is in contact with the ground (for example, the Fth link is the toe link of the support leg), the relative motion of the ground contact coordinate system seen from the whole body coordinate system, and the absolute coordinate system It is possible to obtain the velocity of the center of gravity seen from the following equation.

[Equation 3] However, in the above equation, R0 is the posture matrix of the base link viewed from the absolute coordinate system (that is, the posture transformation matrix of the whole body coordinate system with respect to the absolute coordinate system, 3 × 3 matrix), and 0JF is the origin of the Fth link coordinate system in the whole body coordinate system. Ja concerning relative translational velocity
cobian (3 × n matrix), 0xG is the position vector of the center of gravity in the whole body coordinate system, 0pF is the position vector of the ground link origin in the whole body coordinate system, and 0JωF is the relative rotation speed of the Fth link coordinate system in the whole body coordinate system.
(3 × n matrix).

[0009] 0JF and 0JωF are obtained from a method such as that in the document "Basics of Robotics (Haruhisa Kawasaki, Morikita Publishing, 1991)" and the like. Further, [a ×] is an outer product matrix defined by the following equation with respect to a general vector a = [ax ay az].

[Equation 4]

From the above matters, JG can be obtained from the following equation.

[Equation 5]

The whole body motion of the robot is such that, while operating the center-of-gravity speed, for example, both legs are fixed to the ground, or the tip speed of the swing leg, the hand speed of the work (if having an upper body), the center-of-gravity rotation, and the like. It is generated by satisfying additional constraint conditions for performing various tasks, such as keeping the angular momentum at a specified value. Such constraint conditions can be classified into two types: constraint conditions in the joint angle space and constraint conditions in the non-joint angle space. In the former case, the target velocity refωf of a specific joint angle group θf is directly given. In this case, ω is divided into ωf and the velocity ωu of the remaining joint angle group, and the whole body center of gravity is controlled by ωu. The latter does not directly specify the target value of the joint angle, but is a constraint condition for controlling geometrical or mechanical physical quantities such as the position and posture of the hands and feet, the angular momentum around the center of gravity, and is generally It can be represented by the following equation:

[Equation 6] However, JC = ∂Φ / ∂θ and c = ∂Φ / ∂t.

Now, if a strict target center-of-gravity velocity is given by refvG, the following equation is established when the corresponding target value of all joint angular velocities is set to refω.

[Equation 7] In the above equation, there is no problem even if ω = [ωuT ωfT] T is set for convenience, the target value of ωu is set to refωu, and JG and JC are submatrices [JGuu corresponding to ωf and ωu, respectively.
When decomposed into [JGf] and [JCu JCf], the following equation is derived.

[Equation 8] However, Ju = [JGuT JCuT] T, v = [(ref
vG-JGf refωf) T (c-JCf refω
f) T] T.

Further, in the above equation, when the rank of Ju is r, r independent lines are extracted from Ju and a new Jr is newly extracted.
If u is created and the component of v corresponding to each row is extracted to create vr, the following equation holds.

[Equation 9]

In the above equation, the rank r of Jru and the dimension of ωu do not necessarily match. However, if the weighted generalized inverse matrix Jru # of Jru is used, the target value refωu of all joint angular velocities is obtained by the following equation. You can

[Equation 10] Refωu obtained from the above equation is combined with refωf and re
If fω, the target speed of all joint angles can be obtained.

It should be noted that as shown in the following equation, Δrefθ is obtained by integrating with the control period Δt and added to the current joint angle vector θ, so that the target value r of all joint angles is expressed as an angle instead of an angular velocity.
It is also possible to obtain efθ.

[Equation 11] In the above equation, if Δt is sufficiently small, Δrefθ = r
It may be efωΔt or the like.

In a general multi-legged robot, the grounding link F changes with the replacement of the supporting legs, etc. However, if the F is replaced appropriately each time, there is no problem.

Further, in a general multi-legged robot,
In many cases, there are a plurality of ground links as in the multi-leg support state, in which case one of the ground links may be selected.

[0018]

As described above, according to the present invention, the sensitivity of the velocity of the center of gravity of the legged mobile machine to each joint angle can be obtained exactly. Further, by using it, it becomes possible to instantaneously operate the center-of-gravity velocity of the legged mobile machine with extremely high accuracy while satisfying various constraint conditions added at the same time. Further, the present invention is not limited to a specific mechanism and has sufficient versatility and practicality applicable to a general legged mobile machine.

[Brief description of drawings]

FIG. 1 is a diagram showing a structure of a general multi-legged robot as an example of a legged mobile machine having no fixed points on the ground, an absolute coordinate system, a whole body coordinate system, and a ground coordinate system.

[Explanation of symbols]

Σw absolute coordinate system Σ0 whole body coordinate system ΣF Grounding coordinate system

Claims (3)

[Claims] 1. A method of rigorously determining the sensitivity of the center-of-gravity velocity to each joint angular velocity in a machine having a multi-leg mechanism composed of rigid multi-links connected to a base link, using a physical model of the machine. 2. In a machine having a multi-leg mechanism composed of rigid multi-links connected to a base link, the sensitivity of the center-of-gravity velocity to each joint angular velocity is rigorously determined using a physical model of the machine to determine the center-of-gravity velocity. A method for high-precision operation in real time. 3. In a machine having a multi-leg mechanism composed of rigid multi-links connected to a base link, the sensitivity of the center-of-gravity velocity to each joint angular velocity is rigorously determined using a physical model of the machine, and the toe velocity is further determined. A method for manipulating the center-of-gravity velocity in real time with high precision by using it together with a matrix that describes constraint conditions added to actions such as keeping it at a specified value.