Barycenter position determining method and apparatus, legged robot, and storage medium

A computing device connected to a legged robot, comprising:

• one or more processors;
• and
• memory storing one or more programs, the one or more programs comprising instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:
• creating first relation data, the first relation data indicating a relation between an interval duration t and a center of mass position P(t) of the legged robot, and wherein the center of mass position P(t) varies as a function of the interval duration t and a first constant C according to the first relation data;
• creating second relation data corresponding to the at least one leg of the legged robot, the second relation data indicating a relation between a force fi corresponding to the at least one leg with the ground and the center of mass position P(t), and wherein the force fi corresponding to the at least one leg with the ground varies as a function of the center of mass position P(t) and the first constant C according to the second relation data;
• creating third relation data based on the second relation data, the third relation data indicating a positive correlation between a target value J and a square of the force fi to which the at least one leg in contact with the ground is subjected, wherein the third relation data defines a quadratic programming problem in which the target value J varies as a function of a square of the force fi to which the at least one leg in contact with the ground is subjected;
• solving the quadratic programming problem by (i) applying different values for the first constant C to the center of mass position P(t) according to the first relation data and (ii) applying different values of the center of mass position P(t) corresponding to the different values for the first constant C to the force fi corresponding to the at least one leg with the ground according to the second relation data and (iii) applying different values of the force fi corresponding to the at least one leg with the ground to the target value J according to the third relation data until the target value J is minimized;
• determining, among the different values for the first constant C used for solving the quadratic programming problem, a value of the first constant C when the target value J is minimized as an optimized solution to the quadratic programming problem;
• and
• obtaining the first relation data according to the determined value of the first constant C, wherein the first relation data defines a trajectory of the center of mass position P(t) of the legged robot based on a movement of the legged robot as a function of time.

A non-transitory computer-readable storage medium, storing a computer program, the computer program, when executed by one or more processors of a computing device connected to a legged robot, cause the one or more processors to perform operations comprising:

• creating first relation data, the first relation data indicating a relation between an interval duration t and a center of mass position P(t) of the legged robot, and wherein the center of mass position P(t) varies as a function of the interval duration t and a first constant C according to the first relation data;
• creating second relation data corresponding to the at least one leg of the legged robot, the second relation data indicating a relation between a force fi corresponding to the at least one leg with the ground and the center of mass position P(t), and wherein the force fi corresponding to the at least one leg with the ground varies as a function of the center of mass position P(t) and the first constant (according to the second relation data;
• creating third relation data based on the second relation data, the third relation data indicating a positive correlation between a target value J and a square of the force fi to which the at least one leg in contact with the ground is subjected, wherein the third relation data defines a quadratic programming problem in which the target value J varies as a function of a square of the force fi to which the at least one leg in contact with the ground is subjected;
• solving the quadratic programming problem by (i) applying different values for the first constant C to the center of mass position P(t) according to the first relation data and (ii) applying different values of the center of mass position P(t) corresponding to the different values for the first constant C to the force fi corresponding to the at least one leg with the ground according to the second relation data and (iii) applying different values of the force fi corresponding to the at least one leg with the ground to the target value J according to the third relation data until the target value J is minimized;
• determining, among the different values for the first constant C used for solving the quadratic programming problem, a value of the first constant C when the target value J is minimized as an optimized solution to the quadratic programming problem;
• and
• obtaining the first relation data according to the determined value of the first constant C, wherein the first relation data defines a trajectory of the center of mass position P(t) of the legged robot based on a movement of the legged robot as a function of time.