Method for controlling the walk of humanoid robot

• US 8,738,178 B2
• Filed: 10/24/2005
• Issued: 05/27/2014
• Est. Priority Date: 10/19/2005
• Status: Active Grant

• Current Assignee: Korea Advanced Institute of Science and Technology
• Original Assignee: Korea Advanced Institute of Science and Technology
• Inventors: Choi, Young Jin, Kim, Do Ik, Oh, Yong Hwan, Kim, Chang Hwan, You, Bum Jae, Cho, Jung San
• Primary Examiner(s): Shafi, Muhammad
• Assistant Examiner(s): Malhotra, Sanjeev
• Application Number:
  US12/090,350
• Publication Number:
  US 20080281469A1
• Time in Patent Office: 3,137 Days
• Field of Search: 700/245, 700/250, 700/260, 700/261, 700/262, 700/263, 700/253, 318/568.11, 318/568.12, 318/568.18, 318/568.19, 318/568.2, 901/1, 901/9, 901/23, 180/8.1
• US Class Current: 700/250
• CPC Class Codes: B62D 57/032 with alternately or sequentially lifted supporting base and legs; with alternately or sequentially lifted feet or skid B62D57/024 takes precedence

Abstract

The invention relates to a method for controlling walking of humanoid bipedal walking robot. More specifically, the invention comprises steps of designing a zero momentum position (ZMP) of a robot for the ground surface (a); calculating trajectories of a center of gravity (COG) of the robot along with the trajectory of the ZMP (b); calculating an angular velocity of driving motors of two feet, which has the robot walk according to the trajectory of the ZMP (c); and controlling walking of the robot by driving the driving motors according to the angular velocity of the driving motors calculated above. The robot walking control method according to the invention has stability against disturbances.

Claims

1. A method for controlling walking of a humanoid bipedal walking robot comprising limbs, the method comprising steps of:

(a) designing a desired trajectory of zero momentum position (desired ZMP trajectory) of the robot against the ground surface;

(b) calculating a desired trajectory of a center of gravity (desired COG trajectory) of the robot from the desired ZMP trajectory;

(c) calculating a desired COG motion using the desired COG trajectory;

(d) obtaining usual kinematical Jacobians which represent relations of angular velocities of driving motors of each limb of the robot to velocities of each limb of the robot represented in a world coordinate system and a body center coordinate system;

(e) selecting a base limb to be a supporting leg in the single supporting phase or any one of both of the legs in the double supporting phase;

(f) obtaining a modified COG motion using the desired COG motion based on desired motions of each limb except for the base limb, the usual kinematical Jacobians, and a modified COG Jacobian which represents the relationship between a modified COG velocity and the base limb;

(g) obtaining an angular velocity of a driving motor for the base limb using the modified COG motion and the modified COG Jacobian;

(h) obtaining angular velocities of driving motors for other limbs except for the base limb using the angular velocity of a driving motor for the base limb; and

(i) controlling walking of the robot by driving the driving motors for the limbs of the robot according to the angular velocity of the driving motor for the base limb and according to the angular velocity of the driving motors for the other limbs.

2. The method of claim 1, wherein the desired ZMP trajectory for the walking direction (X-axis direction) p_x(t) of the robot in step (a) is designed as the following Eq. 5:

for 0≦

t<

t_d, p_x(t)=(K_x/t_d)t=c_x(t)

for t_d≦

t<

T−

t_d, p_x(t)=B

for T−

t_d≦

t<

T, p_x(t)=(2B−

K_x)+(K_x/t_d)(t−

(T−

t_d))=c_x(t) 

 

[Eq. 5]

wherein,

T is a single period of walking,

t_d means the change time from a double supporting phase to a single supporting phase in a period,

B is the half of a stride, and

K_x is displacement of the zero momentum position (ZMP) during the t_d, which is determined from Eq. (10);

3. The method of claim 2, wherein the desired ZMP trajectory p_y(t) for the left-right direction (the Y-axis direction) with respect to the walking proceeding direction (the X-Axis direction) in step (a) is designed as Eq. 11:

for 0≦

t<

t_d, p_y(t)=(K_y/t_d)t=c_y(t)

for t_d≦

t<

T−

t_d, p_y(t)=A

for T−

t_d≦

t<

T, p_y(t)=−

(K_y/t_d)(t−

T)=c_y(t) 

 

[Eq. 11]

wherein,

A is half of the distance between the centers of two ankles, and

K_y is the displacement of the ZMP during t_d, which is defined as Eq. (16);

4. The method of claim 2, wherein the desired COG trajectory for the X-axis direction c_x(t) in the step (b)

is equivalent to the desired ZMP trajectory p_x(t) in the double supporting phase, and

is equivalent to the following Eq. 7 in the single supporting phase:

c_x(t)=C_x1 cos h(ω

_n(t−

t_d))+C_x2 sin h(ω

_n(t−

t_d))+B 

 

[Eq. 7]

wherein, the coefficient C_x1 and C_x2 are as the following Eq. 9;

5. The method of claim 3, wherein the desired COG trajectory for the Y-axis direction c_y(t) is equivalent to the desired ZMP trajectory p_y(t) in the double supporting phase, and is equivalent to the following Eq. 13 in the single supporting phase:

c_y(t)=C_y1 cos h(ω

_n(t−

t_d))+C_y2 sin h(ω

_n(t−

t_d))+A 

 

[Eq. 13]

wherein the coefficients C_y1 and C_y2 are as the following Eq. 15;

6. The method of claim 5, wherein the angular velocity of the driving motor for the base limb in the step (g) is obtained by solving the dynamic equation of the following Eq. 25 for all the other limbs except the base limb:

7. The method of claim 6, wherein the angular velocities of the other limbs in the step (h) can be obtained from the following Eq. 22 by using the angular velocity of the driving motor of the base limb:

{dot over (q)}_i=J_i<sup>−

1</sup>{dot over (x)}_i−

J_i<sup>−

1</sup>X_i1({dot over (x)}₁−

J₁{dot over (q)}₁), 

 

[Eq. 22]

for i=1, 2, . . . , n

wherein the relative transformation matrix X_i1 is defined as follows;

8. The method of claim 6, wherein u_i in Eq. 31 wherein ZMP error and COG error are reflected is used as the COG velocity vector of the following Eq. 25:

u_i=ċ

_i^d−

k_p,ie_p,i+k_c,ie_c,i 

 

[Eq. 31]

wherein e_p,i and e_c,i are the ZMP error and the COG error respectively as defined in Eq. 30, and

k_p,i and k_c,I are proportional control gains;

e_p,ip_i^d−

p_i

e_c,ic_i^d−

c_i, for i=x,y. 

 

[Eq. 30]

9. The method of claim 8, wherein the control gain k_p, and satisfy the design condition of Eq. 32: