CN114750162B - High dynamic motion centroid compliant control method for humanoid robot - Google Patents
High dynamic motion centroid compliant control method for humanoid robot Download PDFInfo
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
Abstract
The invention provides a high dynamic motion mass center flexible control method of a humanoid robot, which is based on a linear quadratic regulator design feedback controller and calculates the compensation quantity of mass center momentum second derivative; and integrating the compensation quantity of the centroid momentum second derivative to obtain the compensation quantity of the centroid position and the momentum, superposing the compensation quantity of the centroid position and the momentum on the expected centroid position and the momentum, updating the expected track, and sending the joint track obtained by solving to the robot for execution. According to the method, the compensation quantity of the centroid momentum second derivative is calculated, the feedback coefficient required by the compliant control is obtained, and the time for adjusting the feedback coefficient is effectively reduced; the invention considers the change of the mass line momentum and the angular momentum simultaneously, realizes the flexible control of the mass center in the moving direction and the rotating direction, and improves the stability of the high dynamic motion of the robot.
Description
Technical Field
The invention belongs to the technical field of humanoid robots, and particularly relates to a high-dynamic motion centroid compliant control method of a humanoid robot.
Background
When the humanoid robot is subjected to external disturbance, the stability of the humanoid robot is maintained by adjusting the contact force of the tail end, and because the contact force is closely related to the integral mass center and momentum of the robot, the tail end and mass center of the robot are always required to be flexibly controlled simultaneously when the robot is stably controlled, so that the robot can bear larger continuous external disturbance. At present, the mass center flexible control of the humanoid robot is mainly focused on researching flexible control of mass center movement freedom degree related (namely mass center position and mass center line momentum) movement, and the flexible control of mass center rotation freedom degree related (namely angular momentum around the mass center) movement is not related. Although the angular momentum of the robot about its centroid is negligible when the robot is performing low-speed or static movements (e.g., walking slowly, standing, etc.), the angular momentum about its centroid is not negligible and is critical to the completion of the movement when the robot is performing highly dynamic movements (e.g., running rapidly, jumping, etc.). Therefore, when the robot performs high dynamic motion, the mass center movement and the rotational freedom degree related motion of the robot are required to be flexibly controlled at the same time, so that the robot can realize stable high dynamic motion.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a high dynamic motion centroid compliant control method for a humanoid robot, which realizes the compliant control of the robot centroid state in the moving and rotating directions.
The present invention achieves the above technical object by the following means.
A high dynamic motion mass center compliant control method of a humanoid robot specifically comprises the following steps:
acquiring the floating base pose of the robot, and calculating the actual pose of the contacted tail end;
calculating actual contact resultant force/moment born by the robot according to the actual pose and stress of the contacted robot tail end;
designing a feedback controller based on the linear quadratic regulator, and calculating the compensation quantity of the centroid momentum second derivative;
integrating the compensation quantity of the centroid momentum second derivative to obtain the centroid position and the compensation quantity of the momentum, and updating the expected centroid position and the momentum track by using the centroid position and the compensation quantity of the momentum;
the joint track obtained by solving is sent to a robot for execution;
the compensation quantity of the centroid momentum second derivative is as follows:
wherein ：the compensation quantity of the centroid momentum second derivative is μ as a control quantity, x as a state quantity, K as a feedback coefficient matrix, and the coefficient matrix is +.>Determining a weight matrix Q, R;
the coefficient matrix satisfies:
wherein: contact force/moment error amount = [ ΔfΔτ ]] T Error amount of contact force/moment variationCompensation amount Δh= [ Δh ] of robot momentum l Δh a ] T Compensation for momentum change of robotCompensating amount of momentum second derivative of robot>Error amount of contact resultant forceError amount of contact force variation +.>Error amount of contact resultant moment +.>Error amount of contact resultant moment variation +.> and />Compensation of the second derivative of the centroid linear momentum, angular momentum, respectively, < >> and />Compensation amounts of first order derivatives of centroid line momentum and angular momentum respectively, delta h l and Δha Compensation amount of centroid line momentum and angular momentum respectively, +.> and />Measurement of the desired contact force, the resultant moment of the robot, respectively,/-> and />Desired value of the contact resultant force and the resultant moment of the robot, respectively,/->For the measurement of the contact force variation, +.>For the desired value of the contact force variation, +.>For the measurement of the contact torque variation, +.>T is the lag time, I is the identity matrix;
the weight matrix satisfies:
wherein: j is an objective function.
According to a further technical scheme, the floating base pose of the robot is obtained by reading IMU position and pose measurement values.
According to a further technical scheme, the actual pose of the contacted tail end is as follows:
wherein ,for the actual pose rotation matrix of the tip i in world coordinate system, +.>For the actual position of terminal i under world coordinate system,/->For the actual pose of the robot in the actual coordinate system,/->F is the actual joint angle of the robot K_i (. Cndot.) is a positive kinematic algorithm for determining the pose of any connecting rod from the joint angle, C is the set of the sequence numbers of the contacted ends.
In a further technical solution, the set of contacted terminal serial numbers C is:
wherein ,for the vertical force measurement of the ith end force sensor, f sat Is the contact threshold.
According to a further technical scheme, the actual contact resultant force/moment borne by the robot is as follows:
wherein ,for the actual position of terminal i under world coordinate system,/->Is the actual mass center position of the robot in the world coordinate system, w f i m and />The representation of the forces and moments experienced by the terminal i in the world coordinate system is provided.
According to a further technical scheme, the expected centroid position and the momentum track are updated by utilizing the compensation quantity of the centroid position and the momentum, namely the compensation quantity of the centroid position and the momentum is overlapped on the expected centroid position and the momentum, and the expected track is updated.
In a further technical scheme, the updated track is:
h d* ＝Δh+h d
wherein ,hd Andrespectively the original expected centroid momentum and centroid position, h d* and />The updated desired centroid momentum, centroid position, respectively.
According to a further technical scheme, the joint track angle is obtained by solving the joint angle through inverse kinematics:
wherein ：is the expected joint angular acceleration and joint angle, F IK (. About.) is a humanoid robot inverse kinematics solving method based on quadratic programming>Is the desired tip position and pose.
According to a further technical scheme, the expected contact resultant force and the resultant moment of the robot meet the following conditions:
wherein ： and />The required mass axis momentum change amount and the angular momentum change amount are respectively, M is the robotTotal mass, G, is the gravitational acceleration vector.
The beneficial effects of the invention are as follows:
(1) The invention constructs a linear model of the relation between the actual mass center state and the measured contact force, calculates the feedback coefficient required by the compliant control based on the linear quadratic regulator, effectively reduces the time for regulating the feedback coefficient, and the real-time calculation speed of the feedback controller provided by the invention is far lower than the real-time calculation speed of the quadratic optimization;
(2) According to the invention, expected contact resultant force/moment is calculated, and the mass line momentum variation and angular momentum variation are considered at the same time, so that the flexible control of the mass center in the moving direction and the rotating direction is realized, and the flexible control of the mass center state in the moving direction and the rotating direction is realized when the humanoid robot performs high dynamic motion (the angular momentum of the robot is not negligible), thereby improving the stability of the high dynamic motion of the robot.
Drawings
FIG. 1 is a flow chart of the high dynamic motion centroid compliant control of the humanoid robot of the present invention;
FIG. 2 is a schematic diagram of the centroid forces of the humanoid robot of the present invention;
FIG. 3 is a graph showing the relationship between the local coordinate system of the end and the world coordinate system according to the present invention.
Detailed Description
The invention will be further described with reference to the drawings and the specific embodiments, but the scope of the invention is not limited thereto.
As shown in FIG. 1, the high dynamic motion centroid compliant control method of the humanoid robot comprises the following steps:
step (1), calculating expected contact resultant force/moment according to expected centroid momentum of the current robot;
the invention considers that the expected centroid position and the momentum track are known, and the expected contact resultant force/moment of the robot can be obtained by the humanoid robot mass cardiac mechanics (as shown in figure 2):
wherein , and />Respectively the expected values of the contact resultant force and the resultant moment of the robot; /> and />The angular momentum change quantity is respectively the expected mass axis momentum change quantity and is obtained by differentiating the expected momentum track; m is the total mass of the robot, and the gravity acceleration vector G= [0 0-G ]] T G is gravity acceleration; in fig. 2, f is a contact resultant force, and τ is a contact resultant moment.
Step (2), reading detection values of all end force sensors of the robot, judging whether the end of the robot is in contact with the environment according to the detection values, and acquiring the serial numbers of the contacted ends;
because the force sensor has certain error in measurement and the vertical force applied to the tail end is the largest, the invention uses the vertical force applied to the tail end force sensor as a standard for judging whether the tail end force sensor is in contact with the environment or not, and the judging form is as follows:
wherein ,a vertical force measurement for the ith end force sensor; f (f) sat The touch threshold value can be determined according to the actual application condition of the force sensor;
if formula (2) is satisfied, the i-th end is considered to be in contact with the environment, and if formula (2) is not satisfied, the i-th end is considered to be not in contact with the environment; let the robot end serial number set C meeting the contact be:
step (3), reading IMU positions and gesture measurement values as the floating base gestures of the robot, and calculating the actual gestures of the contacted tail ends;
according to the invention, the position and the posture of the floating base of the humanoid robot in a world coordinate system can be obtained by combining IMU measurement values and a state estimation algorithm (such as extended Kalman filtering, and the like), and then the actual position and the posture of the tail end in contact with the environment can be obtained by solving the positive kinematics algorithm of the humanoid robot:
wherein ,for the actual pose rotation matrix of the tip i in world coordinate system, +.>For the actual position of terminal i under world coordinate system,/->For the actual pose of the robot in the actual coordinate system,/->F is the actual joint angle of the robot K_i (. Cndot.) is a positive kinematic algorithm (Wei Tian Xiusi. Humanoid robot [ M ] for solving any connecting rod pose from joint angle]Guan Yisheng Beijing: university of bloom press, 2007: 50-54) may be used to calculate the tip i pose.
Step (4), calculating actual contact resultant force/moment born by the robot according to the actual pose and the stress of the contacted tail end;
first, the end force sensor measurement is measured under the end local coordinate system, so that the measurement needs to be transferred to the world coordinate system, and the relationship between the end force sensor local coordinate and the world coordinate system is as shown in fig. 3, and then the measurement is converted into the following formula:
wherein ,w f i m andrespectively representing the stress and moment of the tail end i under the world coordinate system, f i m and />The force and moment measured by the force sensor corresponding to the tail end i are respectively; in fig. 3, R is a rotation matrix of the local coordinate system relative to the world coordinate system, and p is a position of an origin of the local coordinate system in the world coordinate system;
then, the force and moment of all the contacted terminals are translated to the centroid to be summed, and the actual contact resultant force/moment can be obtained:
wherein , and />Measurement of the desired contact force, the resultant moment of the robot, respectively,/->The actual mass center position of the robot in the world coordinate system can be obtained by a mature commercial kinematic tool, [] × Representation ofThe vector in square brackets is converted into a diagonal matrix, and I is an identity matrix.
Step (5), calculating the current contact resultant force error of the robot, designing a feedback controller based on a linear quadratic regulator, and calculating the compensation quantity of the centroid momentum second derivative;
since there is typically a lag in actual robot sensor measurements, there is then:
wherein ,true value of the current actual contact force, +.>Desired contact force corresponding to true value of actual contact force, +.>The method is characterized in that the method is a first-order inertia link, T is lag time, and the lag time is determined by the specific running condition of an actual robot; the true value and the expected value corresponding to the current actual contact resultant force are as follows according to centroid dynamics:
wherein ,is a robot mass heartLinear momentum change, ++>The true value of the angular momentum change quantity of the robot around the centroid,for the expected value corresponding to the momentum change of the robot mass axis, < >>The expected value corresponding to the true value of the angular momentum change quantity of the robot around the mass center;
simultaneous (7) and (9), (8) and (10) are available:
and (3) differentiating and sorting the (11) and the (12) to obtain a linear model of the relation between the actual mass center state and the measured contact force:
wherein the contact force/moment error amount Deltaλ= [ DeltafDeltaτ ]] T Error amount of contact force/moment variationCompensation amount Δh= [ Δh ] of robot momentum l Δh a ] T Compensation for momentum change of robotCompensating amount of momentum second derivative of robot>Error amount of contact resultant forceError amount of contact force variation +.>Error amount of contact resultant moment +.>Error amount of contact resultant moment variation +.> Compensation amount for second derivative of centroid linear momentum and angular momentum, ++>Compensation quantity delta h for first order derivative of centroid linear momentum and angular momentum l 、Δh a Compensation amount for centroid line momentum and angular momentum, +.>For the measurement of the contact force variation, +.>For the desired value of the contact force variation, +.>For the measurement of the contact torque variation, +.>Is the expected value of the contact resultant moment variation;
taking the following objective function J:
wherein the state quantityControl amount->Q, R is a weight matrix;
the feedback controller can be designed based on the linear quadratic regulator, so that the compensation quantity of the centroid momentum second derivativeThe method comprises the following steps:
wherein K is a feedback coefficient matrix, which is represented by the coefficient matrix of formula (13) and />) And weight matrix determination of equation (14).
Integrating the compensation quantity to obtain a compensation quantity of the centroid position and the momentum, superposing the compensation quantity of the centroid position and the momentum on a desired centroid position and momentum, and updating a desired track;
and calculating the compensation quantity of the centroid position and the momentum by integration:
wherein Δh is the compensation amount of centroid momentum, and Δx CoG A compensation amount for the centroid position;
superposing (16) on the expected centroid position and the momentum track to obtain an updated track:
wherein ,hd Andrespectively the original expected centroid momentum and centroid position, h d* and />The updated desired centroid momentum, centroid position, respectively.
Step (7), solving inverse kinematics according to the updated expected centroid related track, and sending the obtained joint track to a robot, wherein the robot executes the joint track;
inverse kinematics solves the joint angle:
wherein ,is the expected joint angular acceleration and joint angle, F IK (. Cndot.) is a quadratic programming-based humanoid robot inverse kinematics solving method (K.Bouyarane, et al Quadratic programming for multirobot and task-space force control [ J)].IEEE Transactions on Robotics.2019,35(1):64-77.)，/>The present invention is considered to be known for the desired tip position and pose, given by the planning algorithm.
The examples are preferred embodiments of the present invention, but the present invention is not limited to the above-described embodiments, and any obvious modifications, substitutions or variations that can be made by one skilled in the art without departing from the spirit of the present invention are within the scope of the present invention.
Claims (9)
1. A high dynamic motion mass center compliant control method of a humanoid robot is characterized in that:
acquiring the floating base pose of the robot, and calculating the actual pose of the contacted tail end;
calculating actual contact resultant force/moment born by the robot according to the actual pose and stress of the contacted robot tail end;
designing a feedback controller based on the linear quadratic regulator, and calculating the compensation quantity of the centroid momentum second derivative;
integrating the compensation quantity of the centroid momentum second derivative to obtain the centroid position and the compensation quantity of the momentum, and updating the expected centroid position and the momentum track by using the centroid position and the compensation quantity of the momentum;
the joint angle obtained by solving is sent to a robot for execution;
the compensation quantity of the centroid momentum second derivative is as follows:
wherein ：the compensation quantity of the centroid momentum second derivative is μ as a control quantity, x as a state quantity, K as a feedback coefficient matrix, and the coefficient matrix is +.>Determining a weight matrix Q, R;
the coefficient matrix satisfies:
wherein: contact force/moment error amount = [ ΔfΔτ ]] T Error amount of contact force/moment variationCompensation amount Δh= [ Δh ] of robot momentum l Δh a ] T Compensation for momentum change of robotCompensating amount of momentum second derivative of robot>Error amount of contact resultant forceError amount of contact force variation +.>Error amount of contact resultant moment +.>Error amount of contact resultant moment variation +.> and />Compensation of the second derivative of the centroid linear momentum, angular momentum, respectively, < >> and />Compensation amounts of first order derivatives of centroid line momentum and angular momentum respectively, delta h l and Δha Compensation amount of centroid line momentum and angular momentum respectively, +.> and />Measurement of the desired contact force, the resultant moment of the robot, respectively,/-> and />Desired value of the contact resultant force and the resultant moment of the robot, respectively,/->For the measurement of the contact force variation, +.>For the desired value of the contact force variation, +.>For the measurement of the contact torque variation, +.>T is the lag time, I is the identity matrix;
the weight matrix satisfies:
wherein: j is an objective function.
2. The method for compliant control of the centroid of high dynamic motion of a humanoid robot of claim 1 wherein the floating base pose of the robot is obtained by reading IMU position and pose measurements.
3. The method for flexibly controlling the mass center of motion of the humanoid robot according to claim 2, wherein the actual pose of the contacted end is:
wherein ,for the actual pose rotation matrix of the tip i in world coordinate system, +.>For the actual position of terminal i under world coordinate system,/->For the actual pose of the robot in the actual coordinate system,/->F is the actual joint angle of the robot K_i (. Cndot.) is a positive kinematic algorithm for determining the pose of any connecting rod from the joint angle, C is the set of the sequence numbers of the contacted ends.
4. The method for compliant control of the centroid of motion of a humanoid robot according to claim 3, wherein the set of contacted end sequence numbers C is:
wherein ,for the vertical force measurement of the ith end force sensor, f sat Is the contact threshold.
5. The method for flexibly controlling the mass center of motion of the humanoid robot according to claim 1, wherein the actual contact resultant force/moment applied to the robot is:
wherein ,for the actual position of terminal i under world coordinate system,/->Is the actual mass center position of the robot in the world coordinate system, w f i m and />The representation of the forces and moments experienced by the terminal i in the world coordinate system is provided.
6. The method for flexibly controlling the centroid of the humanoid robot with high dynamic motion according to claim 1, wherein the updating of the expected centroid position and the momentum trajectory by using the compensation amount of the centroid position and the momentum is to superimpose the compensation amount of the centroid position and the momentum on the expected centroid position and the momentum, and update the expected trajectory.
7. The method for flexibly controlling the mass center of motion of the humanoid robot according to claim 6, wherein the updated trajectory is:
h d* ＝Δh+h d
wherein ,hd Andrespectively the original expected centroid momentum and centroid position, h d* and />The updated desired centroid momentum, centroid position, respectively.
8. The method for flexibly controlling the mass center of motion of the humanoid robot according to claim 7, wherein the joint track angle is obtained by solving the joint angle through inverse kinematics:
wherein ：is the expected joint angular acceleration and joint angle, F IK (. About.) is a humanoid robot inverse kinematics solving method based on quadratic programming>Is the desired tip position and pose.
9. The method for flexibly controlling the mass center of motion of the humanoid robot according to claim 1, wherein the expected contact resultant force and the expected contact resultant moment of the robot satisfy:
wherein ： and />Respectively is of a period ofThe change amount of the moment of the line of sight mass and the change amount of the angular moment are shown in the specification, M is the total mass of the robot, and G is a gravity acceleration vector.
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