JP3536084B2 - Gait control method for walking robot - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an optimal walking technique for a walking robot.

[0002]

2. Description of the Related Art Conventionally, a target trajectory of leg motion of a legged robot has been generally calculated offline in advance so as to satisfy ZMP, and trajectory tracking control is generally performed.

[0003]

However, in order to calculate the target trajectory in advance offline, the designer must come up with a trajectory that satisfies ZMP. ZMP is the formula (2),
Or when it can write like (3) type | formula, the input with respect to ZMP is not decided uniquely, and is not necessarily optimal.
This is to determine XZMP

[0004]

[Expression 1]

This is because it is necessary to decide.

Here, let us consider a conventional technique for stabilizing ZMP. In general, ZMP on the x-axis when there are n links is represented by the following equation.

[0007]

[Expression 2]

Here, the above equation can be easily expressed by representing the center of gravity of the entire robot.

[0009]

[Equation 3]

[0010] The physical meaning is easy to understand when considering the one-mass system model of equation (3). Here, for example, assuming that the position of the center of gravity is kept at a constant altitude h _ref ,

[0011]

[Expression 4]

(3) is

[Equation 5] It becomes. Therefore, the center of gravity acceleration

[0013]

[Formula 6]

If the input can be made as in the above, a restoring torque is obtained so that the actual total floor reaction force converges to the target ZMP. Such a robot control method has been considered until recently. However, the intention of the designer has entered the place where the height of the center of gravity is kept constant. This is because the ZMP cannot be uniquely determined unless the altitude is constant in equation (3). After all, in the conventional method, the ZMP is derived by a pseudo method such as maintaining a constant altitude.

The present invention has been made in view of the above-described circumstances, and an object thereof is a gait control method for a walking robot that enables ZMP optimum leg movement in real time by a real time optimization method. .

[0016]

In response to this object, the gait control method for a walking robot according to the present invention provides zero moment point control by receiving horizon control (Receeding).
Horizon Control) is used to generate a target trajectory in real time.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described in detail with reference to the drawings showing an embodiment.

The target trajectory of the walking robot is a zero moment point (ZMP) received by a receiving horizon control (Receding H).
orizon control-RHC).

RHC is a real-time optimal control technique, and its algorithm and the like are described in the literature (Takeuchi, Otsuka:
Optimization calculation of mechanical link system using Receding Horizon Control -Study on numerical solution using continuous deformation method-, Journal of the Robotics Society of Japan, vo
l. 17, no. 3, 1999).
Conventional optimization methods (typically gradient methods) that do not rely on RHC cannot use real gradients to derive optimal solutions in real time. For example, in order to control for 5 seconds, it may take many hours or tens of hours to obtain the optimum trajectory. The formulation of the optimal control problem is that the time interval to be evaluated is infinite (conventional method) or is finite and the evaluation interval moves (RHC). Therefore, the equation (9) is set as the evaluation function, the equation (7) is set as the state equation of the system, and the general optimal control problem is that there are conditions of the initial state of the start point and the state of the end point. . In the present invention, the equation constraint condition (10) is added to this. As a result, the ZMP can follow the target ZMP in a strict sense. This is because the expression (10) is included in the Hamiltonian like the expression (11). (1
0) The first term in the equation represents the target ZMP, and the second and subsequent terms represent the current ZMP. When these two are equal, it becomes an equality constraint condition.

A legged robot is modeled as shown in FIGS.

[0021]

[Expression 7] However,

[Equation 8]

It is. θ is the rotation angle of the joint, u is the joint torque, X is a state variable, U is an input variable, and t is time. As an evaluation function,

[0023]

[Equation 9]

Suppose that φ (Tf) is a terminal constraint. Furthermore, when ZMP is applied with a representative center of gravity as in equation (3),

[Expression 10]

[0025]

## EQU11 ##

In this way, from the optimum input U,

[0027]

[Expression 12]

Can be derived. This is the ideal translational acceleration obtained from the optimal solution.

[0029]

[Expression 16]

[0030]

[Formula 13]

Only the equation (1) has an x-axis and a z-axis and is not uniquely determined. there,

[0032]

If z = h (constant) (14),

[0033]

[Expression 15]

Then the above equation becomes

[0035]

[Expression 16]

Then, So, for example

[0037]

[Expression 17]

At that time, as shown in FIG.

[0039]

[Formula 18]

Thus, if the center of gravity is accelerated forward, Xzm
p increases. vice versa,

[0041]

[Equation 19]

At this time, as shown in FIG.
According to 8), Xzmp decreases if the vehicle is decelerated backward.
The latest ZMP control method is to make the ZMP follow the target ZMP trajectory using these two effects.

However, in this method, operation input is performed by a pseudo measure of Z = h (constant).

The problem is that it is not an essential solution because ## EQU18 ## is obtained. (2) Proposed method of the present invention In the proposed method, the condition that Z = h (constant) is not used, so that an optimal solution satisfying the equality constraint can be obtained. According to this method, the following two items can be achieved.

[0044]

[Expression 20]

As shown in FIG. 5, the optimum target trajectory between the start point and the end point can be generated, and control using the optimum state feedback of the RHC can be performed at each time. Generation of optimal target trajectory between start point and end point This can be calculated all at once on an off-line computer, or can be sequentially calculated in real time.

[0046]

[Expression 21]

For example, for example,

[0048]

[Expression 22]

The robot can be moved by constructing the following control system. R at each time
Use HC optimal state feedback.

This is to make the RHC real-time control as shown in FIG. In the conventional method (Equation 1
In response to the over-deceleration of 8), the optimal state feedback law of RHC outputs a joint torque that satisfies (Equation 20). This is input directly to the actuator. In the conventional method, processing in one dimension of the x axis can be processed in two dimensions of x and z.

Various evaluation functions can be considered when this RHC is used. Typical and simple functions are as follows:

[0052]

[Expression 23]

. That is, the sum of squares of each joint torque is taken.

[0054]

As described above, according to the present invention, it is possible to obtain a gait control method for a walking robot that enables real-time optimal target trajectory generation and ZMP real-time optimal control.

[0055]

[Brief description of the drawings]

FIG. 1 is a diagram showing the definition of ZMP.

FIG. 2 is a diagram showing a leg model.

FIG. 3 is an explanatory diagram showing positions of a zero moment point and a target zero moment point in a single leg support period.

FIG. 4 is an explanatory diagram showing positions of a zero moment point and a target zero moment point.

FIG. 5 is an explanatory diagram showing an optimum target trajectory.

FIG. 6 is an explanatory diagram showing control using optimum state feedback of the RHC at each time.

   ──────────────────────────────────────────────────── ─── Continued front page       (56) References JP-A-5-305581 (JP, A)                 JP 4-201186 (JP, A)                 Takeuchi, Otsuka: Receding Ho               Machine using rison Control               Optimal calculation of mechanical link system-continuous deformation method               On numerical solution using GIS               Journal of the Bot Society, Vol. 17, no. 3,               1999

Claims (1)

(57) [Claims] 1. A robot gait control method for generating a target trajectory of a leg motion of a walking robot in real time by performing zero moment point (ZMP) control by receiving horizon control, wherein: For horizon control, target ZMP and ZMP
Equation 1 below, which is the equality constraint condition where the current values are equal
Is included in the Hamiltonian as shown in Equation 2 below, thereby enabling the ZMP current location to follow the target ZMP. [Expression 1] [Expression 2]