CN112925320A - Biped robot gait energy consumption assessment method based on centroid model - Google Patents

Biped robot gait energy consumption assessment method based on centroid model Download PDF

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CN112925320A
CN112925320A CN202110100346.9A CN202110100346A CN112925320A CN 112925320 A CN112925320 A CN 112925320A CN 202110100346 A CN202110100346 A CN 202110100346A CN 112925320 A CN112925320 A CN 112925320A
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biped robot
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energy consumption
centroid
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卢志强
侯媛彬
柴秀丽
孟芸
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Henan University
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Abstract

The invention relates to a biped robot gait energy consumption assessment method based on a centroid model, which comprises the steps of firstly establishing the centroid model according to the distribution position of the mass M of the biped robot on a body, describing the motion track of the biped robot by using the centroid model, secondly establishing a joint actuator load torque equation by the Cartesian product of a space position vector and a centroid gravity vector in the motion process of the biped robot, and obtaining the axial load torque tau (n) of a joint actuator based on the axis direction of the joint actuator, and finally establishing an energy consumption index function E according to the angular speed omega (n) and the axial load torque tau (n) of the joint actuator of the biped robot in the motion process of the biped robot. The invention overcomes the problem that the instantaneous power loss of each joint actuator of the biped robot is difficult to measure, and the parameters which are easy to obtain in the motion planning algorithm of the biped robot are used for constructing the index function for describing the energy consumption in the motion process of the robot, so that the advantages and disadvantages of different algorithms can be quickly and accurately evaluated.

Description

Biped robot gait energy consumption assessment method based on centroid model
Technical Field
The invention relates to the field of biped robot motion design, in particular to a biped robot gait energy consumption assessment method based on a centroid model.
Background
The energy consumption generated in the motion process of the biped robot comprises motion loss for driving the joint actuator to operate and non-motion energy consumption for the work of the sensor and the controller. In general, the kinematic losses are the major component of the system energy consumption, and their value is the integral of all the joint actuator instantaneous power vectors over time, and the non-kinematic energy consumption generally appears as a linear function of time.
The biped robot is generally composed of a plurality of joint actuator driving connecting rods, and the accurate measurement of the instantaneous power of the joint actuator is not easy. Considering that the instantaneous power of the joint actuator is equal to the sum of the output power of the joint actuator and the additional loss, the output power of the joint actuator as a main component can be regarded as the product of the output torque of the joint actuator and the angular velocity of the joint actuator, and when the biped robot moves, the output torque of the motor is used for overcoming the resistance of the load torque to the rotating shaft of the actuator.
Under general conditions, the angular speed and the load torque of the joint actuator in the motion planning process of the biped robot are easy to obtain, if an energy consumption function of the motion planning algorithm of the biped robot is constructed on the basis of the angular speed and the load torque of the joint actuator, the energy consumption function can be quickly calculated by applying a computer simulation technology in the algorithm optimization process, and the method is suitable for evaluating the advantages and the disadvantages of different motion planning algorithms.
Disclosure of Invention
The invention provides a biped robot gait energy consumption assessment method based on a centroid model for assessing the gait energy consumption of the conventional biped robot, and the energy consumption assessment of a biped robot gait planning algorithm is realized by establishing an energy consumption index function E according to the angular velocity omega (n) and the axial load torque tau (n) of a joint actuator of the biped robot.
The invention provides a biped robot gait energy consumption assessment method based on a centroid model, which comprises the following steps:
step 1: establishing a mass center model according to the distribution position of the mass M of the biped robot on the body, and describing the motion trail of the biped robot by using the mass center model;
step 2: constructing a joint actuator load torque equation through a Cartesian product of a space position vector and a mass center gravity vector in the motion process of the biped robot, and obtaining an axial load torque tau (n) of the joint actuator based on the axis direction of the joint actuator;
and step 3: and in a gait cycle N, establishing an energy consumption index function E according to the angular velocity omega (N) and the axial load torque tau (N) of the joint actuator of the biped robot, wherein the energy consumption index function E is used for evaluating the gait energy consumption of the biped robot.
Further, the step 1 specifically includes:
step 1.1: according to the distribution position of the mass M of the biped robot on the body, a mass center model is established through a formula (1):
Figure BDA0002913320800000021
wherein m isjRepresents the jth centroid of the biped robot, j being 1, 2, …, K;
step 1.2: according to the mass center m of the biped robotjAnd the position of the sampling point at the n moment in the motion process of the biped robot
Figure BDA0002913320800000022
Respectively constructing a centroid vector m and a centroid position matrix Rm(n) represented by formulas (2) and (3):
m＝[m1 m2 … mK] (2)；
Figure BDA0002913320800000023
further, the step 2 specifically includes:
step 2.1: on the premise of no loss of generality, the biped robot is composed of connecting rods driven by L joint actuators, and the position of the ith joint actuator in the motion process of the biped robot is
Figure BDA0002913320800000024
The ith joint actuator load torque
Figure BDA0002913320800000025
As expressed by equation (4):
Figure BDA0002913320800000026
wherein the content of the first and second substances,
Figure BDA0002913320800000027
representing a spatial position vector between the ith joint actuator position and the jth centroid position,
Figure BDA0002913320800000028
is the jth centroid gravity vector,
Figure BDA0002913320800000029
g＝9.81m/s2，
Figure BDA00029133208000000210
support coefficient of link driven by ith joint actuator to jth mass center
Figure BDA00029133208000000211
Indicating full support, coefficient of support
Figure BDA00029133208000000212
Representing shared support, support coefficient
Figure BDA00029133208000000213
Representing no support, the joint actuator load torque is represented as the sum of the cartesian products of the spatial position vector and the centroid gravity vector;
step 2.2: the axial unit vector of the ith joint actuator in the motion of the biped robot is
Figure BDA00029133208000000214
Based on equation (4), the axial load torque τ of the ith joint actuatori(n) is expressed as formula (5):
Figure BDA00029133208000000215
further, the step 3 specifically includes:
step 3.1: under the premise of no loss of generality, in the motion process of the biped robot, the corresponding angles of the ith joint actuator at the sampling point n and n-1 are q respectivelyi(n) and qi(n-1), the angular velocity ω of the ith joint actuatori(n) is expressed as formula (6):
Figure BDA00029133208000000216
wherein, tsSampling period of robot motion control system;
step 3.2: in the motion process of the biped robot, an angular velocity vector omega (n) and an axial load torque vector tau (n) of a joint actuator are respectively expressed as follows:
ω(n)＝[ω1(n) ω2(n) … ωL(n)] (7)；
τ(n)＝[τ1(n) τ2(n) … τL(n)] (8)；
step 3.3: when the gait cycle of the biped robot motion planning is N, establishing an energy consumption index function E by the angular speed omega (N) and the axial load torque tau (N) of the joint actuator, as represented by the formula (9):
Figure BDA0002913320800000031
wherein s (n) diag(s)1(n)，s2(n)，…sL(n)) is an L-order diagonal matrix for representing the directional relationship between the angular velocity vector ω (n) and the axial load torque τ (n), if si(n) 0 represents τi(n) and ωi(n) in the same direction, i.e. gravity forces the joint actuator to move if si(n) 1 represents τi(n) and ωi(n) opposite directions, i.e., the joint actuator moves against gravity.
Through the technical scheme, the invention has the beneficial effects that:
the method describes the motion track of the biped robot through a centroid model, further obtains the axial load torque tau (n) of the joint actuator of the biped robot and the angular speed omega (n) of the joint actuator of the biped robot, establishes an energy consumption index function E based on the angular speed omega (n) and the axial load torque tau (n) of the joint actuator of the biped robot through stress analysis, calculates the gait track energy consumption of each sampling point of the biped robot by using the energy consumption index function E, and finally realizes the evaluation of the gait energy consumption of the biped robot.
According to the method, the gait energy consumption of the biped robot of the centroid model is evaluated by establishing the energy consumption index function E, the problem that the instantaneous power consumption of each joint actuator of the biped robot is difficult to measure is solved, the analysis is convenient to be carried out by combining the gait, so that the accuracy of the energy consumption evaluation of the biped robot of the centroid model is greatly improved, and a reliable foundation is provided for the gait algorithm optimization of the biped robot of the centroid model.
Drawings
FIG. 1 is a flow chart of a gait energy consumption evaluation method of a biped robot based on a centroid model.
FIG. 2 is a diagram of a humanoid robot used by a verification algorithm of the gait energy consumption evaluation method of the biped robot based on the centroid model.
Fig. 3 is a variable schematic diagram of the biped robot energy consumption evaluation method of the biped robot gait energy consumption evaluation method based on the centroid model.
Fig. 4 is a motion simulation diagram of the biped robot of the gait energy consumption evaluation method of the biped robot based on the centroid model.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, an embodiment of the present invention provides a gait energy consumption evaluation method for a biped robot based on a centroid model, the method includes the following steps:
step 1: establishing a mass center model according to the distribution position of the mass M of the biped robot on the body, and describing the motion trail of the biped robot by using the mass center model;
step 2: constructing a joint actuator load torque equation through a Cartesian product of a space position vector and a mass center gravity vector in the motion process of the biped robot, and obtaining an axial load torque tau (n) of the joint actuator based on the axis direction of the joint actuator;
and step 3: and in a gait cycle N, establishing an energy consumption index function E according to the angular velocity omega (N) and the axial load torque tau (N) of the joint actuator of the biped robot, wherein the energy consumption index function E is used for evaluating the gait energy consumption of the biped robot.
The method is used for describing the motion trail of the biped robot through the position of a joint actuator and the position of a mass center in the motion of the biped robot so as to determine the energy consumption in the motion of the biped robot, and further establishing an energy consumption index function E according to the angular speed omega (n) and the axial load torque tau (n) of the joint actuator of the biped robot;
the error caused by directly measuring the instantaneous power of the joint actuator by using a sensor is avoided, and the energy consumption value of each sampling point in the motion of the biped robot is convenient to grasp and determine, so that an energy consumption evaluation model of the biped robot is constructed;
example 2
On the basis of the embodiment 1, the embodiment of the present invention is different from the embodiment in that the method optimizes the step 1 and establishes the biped robot of the K centroid model, specifically:
step 1.1: according to the distribution position of the mass M of the biped robot on the body, a mass center model is established through a formula (1):
Figure BDA0002913320800000041
wherein m isjRepresents the jth centroid of the biped robot, j being 1, 2, …, K;
step 1.2: according to the mass center m of the biped robotjAnd the position of the sampling point at the n moment in the motion process of the biped robot
Figure BDA0002913320800000042
Respectively constructing a centroid vector m and a centroid position matrix Rm(n) represented by formulas (2) and (3):
m＝[m1 m2 … mK] (2)；
Figure BDA0002913320800000051
example 3
On the basis of the above embodiment 2, the difference between the embodiment of the present invention and the above embodiment is that, as shown in fig. 3, in order to obtain the axial load torque vector τ (n) of the joint actuator, the step 2 is optimized, specifically:
step 2.1: on the premise of no loss of generality, the biped robot is composed of connecting rods driven by L joint actuators, and the position of the ith joint actuator in the motion process of the biped robot is
Figure BDA0002913320800000052
The ith joint actuator load torque
Figure BDA0002913320800000053
As expressed by equation (4):
Figure BDA0002913320800000054
wherein the content of the first and second substances,
Figure BDA0002913320800000055
representing a spatial position vector between the ith joint actuator position and the jth centroid position,
Figure BDA0002913320800000056
is the jth centroid gravity vector,
Figure BDA0002913320800000057
g＝9.81m/s2，
Figure BDA0002913320800000058
support coefficient of link driven by ith joint actuator to jth mass center
Figure BDA0002913320800000059
Indicating full support, coefficient of support
Figure BDA00029133208000000510
Representing shared support, support coefficient
Figure BDA00029133208000000511
Representing no support, the joint actuator load torque is represented as the sum of the cartesian products of the spatial position vector and the centroid gravity vector;
step 2.2: the axial unit vector of the ith joint actuator in the motion of the biped robot is
Figure BDA00029133208000000512
Based on equation (4), the axial load torque τ of the ith joint actuatori(n) is expressed as formula (5):
Figure BDA00029133208000000513
example 4
On the basis of the above embodiments, the difference between the embodiment of the present invention and the above embodiments is that, in order to obtain the angular velocity vector ω (n) of the joint actuator, and create the consumption index function E based on the angular velocity vector ω (n) of the joint actuator, step 3 is optimized, specifically:
step 3.1: under the premise of no loss of generality, in the motion process of the biped robot, the corresponding angles of the ith joint actuator at the sampling point n and n-1 are q respectivelyi(n) and qi(n-1), the angular velocity ω of the ith joint actuatori(n) is expressed as formula (6):
Figure BDA00029133208000000514
wherein, tsSampling period of robot motion control system;
step 3.2: in the motion process of the biped robot, an angular velocity vector omega (n) and an axial load torque vector tau (n) of a joint actuator are respectively expressed as follows:
ω(n)＝[ω1(n) ω2(n) … ωL(n)] (7)；
τ(n)＝[τ1(n) τ2(n) … τL(n)] (8)；
step 3.3: when the gait cycle of the biped robot motion planning is N, establishing an energy consumption index function E by the angular speed omega (N) and the axial load torque tau (N) of the joint actuator, as represented by the formula (9):
Figure BDA0002913320800000061
wherein s (n) diag(s)1(n)，s2(n)，…sL(n)) is an L-order diagonal matrix for representing the directional relationship between the angular velocity vector ω (n) and the axial load torque τ (n), if si(n) 0 represents τi(n) and ωi(n) in the same direction, i.e. gravity forces the joint actuator to move if si(n) 1 represents τi(n) and ωi(n) opposite directions, i.e. movement of the joint actuator against gravity。
The following experiments were conducted to demonstrate the effects of the present invention
As shown in figure 2, the biped (humanoid) robot is constructed to include a body centroid M according to the distribution position of the mass M on the body1Mass center m of two legs2And m3Mass center m of both feet4And m5The five centroid model of (1). The legs of the biped robot are of a multi-link structure with 10 links, and respectively comprise hip joint rolling control q1And q is2Hip joint pitch control q3And q is4Knee joint pitch angle q5And q is6Ankle joint pitch angle q7And q is8And ankle joint roll angle q9And q is10；
Further as shown in fig. 3, the centroid position of the biped robot
Figure BDA0002913320800000062
Joint actuator position
Figure BDA0002913320800000063
And joint actuator axial direction
Figure BDA0002913320800000064
Wherein g is 9.81m/s2The barycenter vector m of the biped robot is (m)1 m2 … m5]The values of (a) are shown in table 1:
TABLE 1 center of mass of biped robot
Figure BDA0002913320800000065
In order to express the rationality of the energy consumption evaluation method, in the motion planning of the biped robot, the step length s is 10cm, the gait cycle N is 16, and the sampling period t is selectedsA set of gait data of 0.1s, wherein the center of mass position R is in the motion process of the biped robotmThe x-direction and y-direction components of (n) are shown in table 2:
TABLE 2 center of mass of biped robot in motion processPosition Rm(n) (unit: cm)
Figure BDA0002913320800000071
Further, the position R of the joint actuator during the movementa(n) the X-direction component is shown in Table 3, and the Joint actuator position RaThe y-direction component of (n) is shown in Table 4:
TABLE 3 Joint actuator position R in biped robot motionaX component of (n) (unit: cm)
Figure BDA0002913320800000072
Figure BDA0002913320800000081
TABLE 4 Joint executor position R in biped robot motion processaY component of (n) (unit: cm)
Figure BDA0002913320800000082
Figure BDA0002913320800000091
Further, the joint actuator load torque τ (n) during motion is shown in table 5:
TABLE 5 axial load of joint actuator during biped robot motion Joint actuator load torque τ (N) (unit: N cm)
Figure BDA0002913320800000092
Further, the angular velocity ω (n) of the joint actuator during motion is shown in table 6:
TABLE 6 angular velocity ω (n) (unit: 0.01rad/s) of the joint actuator in the biped robot motion process
Figure BDA0002913320800000093
Figure BDA0002913320800000101
Through the data shown in tables 1-6, based on the method, the motion energy consumption of the biped robot in the gait cycle N is calculated, and then the gait energy consumption evaluation of the biped robot is realized, as shown in fig. 4, the biped robot is subjected to motion simulation, and finally the energy consumption index function E of the biped robot is 11.35J.
The above-described embodiments are merely preferred embodiments of the present invention, and not intended to limit the scope of the invention, so that equivalent changes or modifications in the structure, features and principles described in the present invention should be included in the claims of the present invention.

Claims (4)

1. A gait energy consumption assessment method of a biped robot based on a centroid model is characterized by comprising the following steps:
step 1: establishing a mass center model according to the distribution position of the mass M of the biped robot on the body, and describing the motion trail of the biped robot by using the mass center model;
step 2: constructing a joint actuator load torque equation through a Cartesian product of a space position vector and a mass center gravity vector in the motion process of the biped robot, and obtaining an axial load torque tau (n) of the joint actuator based on the axis direction of the joint actuator;
and step 3: and in a gait cycle N, establishing an energy consumption index function E according to the angular velocity omega (N) and the axial load torque tau (N) of the joint actuator of the biped robot, wherein the energy consumption index function E is used for evaluating the gait energy consumption of the biped robot.
2. The gait energy consumption assessment method of the biped robot based on the centroid model as claimed in claim 1, wherein the step 1 specifically comprises:
step 1.1: according to the distribution position of the mass M of the biped robot on the body, a mass center model is established through a formula (1):
Figure FDA0002913320790000011
wherein m isjRepresents the jth centroid of the biped robot, j being 1, 2, …, K;
step 1.2: according to the mass center m of the biped robotjAnd the position of the sampling point at the n moment in the motion process of the biped robot
Figure FDA0002913320790000012
Respectively constructing a centroid vector m and a centroid position matrix Rm(n) represented by formulas (2) and (3):
Figure FDA0002913320790000013
Figure FDA0002913320790000017
3. the method for evaluating the energy consumption of the biped robot based on the centroid model of the centroid as claimed in claim 1, wherein the step 2 specifically comprises:
step 2.1: on the premise of no loss of generality, the biped robot is composed of connecting rods driven by L joint actuators, and the position of the ith joint actuator in the motion process of the biped robot is
Figure FDA0002913320790000014
The ith joint actuator load torque
Figure FDA0002913320790000015
As expressed by equation (4):
Figure FDA0002913320790000016
wherein the content of the first and second substances,
Figure FDA0002913320790000021
representing a spatial position vector between the ith joint actuator position and the jth centroid position,
Figure FDA0002913320790000022
is the jth centroid gravity vector,
Figure FDA0002913320790000023
g＝9.81m/s2，
Figure FDA0002913320790000024
support coefficient of link driven by ith joint actuator to jth mass center
Figure FDA0002913320790000025
Indicating full support, coefficient of support
Figure FDA0002913320790000026
Representing shared support, support coefficient
Figure FDA0002913320790000027
Representing no support, the joint actuator load torque is represented as the sum of the cartesian products of the spatial position vector and the centroid gravity vector;
step 2.2: the axial unit vector of the ith joint actuator in the motion of the biped robot is
Figure FDA0002913320790000028
Based on equation (4), the axial load torque τ of the ith joint actuatori(n) is expressed as formula (5):
Figure FDA0002913320790000029
4. the gait energy consumption assessment method of the biped robot based on the centroid model as claimed in claim 3, wherein the step 3 specifically comprises:
step 3.1: under the premise of no loss of generality, in the motion process of the biped robot, the corresponding angles of the ith joint actuator at the sampling point n and n-1 are q respectivelyi(n) and qi(n-1), the angular velocity ω of the ith joint actuatori(n) is expressed as formula (6):
Figure FDA00029133207900000210
wherein, tsSampling period of robot motion control system;
step 3.2: in the motion process of the biped robot, an angular velocity vector omega (n) and an axial load torque vector tau (n) of a joint actuator are respectively expressed as follows:
ω(n)＝[ω1(n) ω2(n) … ωL(n)] (7)；
τ(n)＝[τ1(n) τ2(n) … τL(n)] (8)；
step 3.3: when the gait cycle of the biped robot motion planning is N, establishing an energy consumption index function E by the angular speed omega (N) and the axial load torque tau (N) of the joint actuator, as represented by the formula (9):
Figure FDA00029133207900000211
wherein s (n) diag(s)1(n)，s2(n)，…sL(n)) is an L-order diagonal matrix for representing the directional relationship between the angular velocity vector ω (n) and the axial load torque τ (n), if si(n) 0 represents τi(n) and ωi(n) in the same direction, i.e. gravity forces the joint actuator to move if si(n) 1 represents τi(n) and ωi(n) opposite directions, i.e., the joint actuator moves against gravity.
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