A path tracking method for a spherical multi-elastic leg robot

Abstract

A path tracking method for a spherical multi-legged robot belongs to the field of mobile robot motion control technology. The steps are as follows: Step 1: Establish the robot's kinematic model; Step 2: Calculate the contact forces acting on the robot and establish a dynamic model; Step 3: Based on the robot's real-time motion, two methods for determining the motion direction are designed: if the robot is inside the path, the motion direction is determined using the perpendicular direction of the tangent related to the path; if the robot is outside the path, the motion direction is determined using the tangent and intercept directions related to the path; Step 4: The extension and retraction of the legs are determined by the critical states of the two robot movements. This invention provides a real-time and effective control scheme for the robot's position. This invention can solve the problems of the inability to perform real-time robot control and the large motion errors when facing complex paths.

Description

Technical Field

[0001] This invention belongs to the field of mobile robot motion control technology, specifically relating to a path tracking method for a spherical multi-extended legged robot. Background Technology

[0002] In the field of mobile robotics, the spherical multi-legged robot is a multifunctional robot that can traverse uncertain terrain, inspired by creatures in nature that move by rolling.

[0003] For spherical multipedal robots, existing research has proposed two motion planning schemes: the discrete method and the inverse kinematics method. Hiroki et al. [Nozaki, Hiroki, et al. "Shape changing locomotion by spinymultipedal robot." 2017 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE, 2017.] designed a rolling locomotion state (Shape Changing Locomotion by Spiny Multipedal Robot) for a twelve-legged robot, achieving rolling motion through shape transformation. The discrete method severely restricts the direction and distance of movement for each step, failing to fully utilize the robot's potential for omnidirectional motion, and the manual planning process is quite cumbersome. Hiroki et al. [Nozaki, Hiroki, et al. "Continuous shape changing locomotion of 32-legged spherical robot." 2018 IEEE / RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2018.] drew inspiration from the locomotion of amoebas (Continuous Shape Changing Locomotion of 32-legged Spherical Robot) and proposed an inverse kinematics method. This method assumes that the robot has a smooth imaginary membrane, and achieves continuous gait by adjusting the length of the legs according to the membrane contact conditions. The inverse kinematics method does not consider the contact forces between the legs and the ground, resulting in the robot's movement path being larger than expected.

[0004] Therefore, existing motion planning schemes do not provide real-time control for robots, resulting in significant motion errors when facing complex paths. Summary of the Invention

[0005] The purpose of this invention is to provide a path tracking method for a spherical multi-extended legged robot, which controls the robot's position in real time and solves the problems of not being able to control the robot in real time and having large motion errors when facing complex paths.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A path tracking method for a spherical multi-legged robot includes the following steps: First, establishing a kinematic model of the robot; second, calculating the contact forces acting on the robot and establishing a dynamic model; third, designing two methods to determine the motion direction based on the robot's real-time motion: if the robot is inside the path, the motion direction is determined using the tangent and perpendicular directions related to the path; if the robot is outside the path, the motion direction is determined using the tangent and secant directions related to the path; finally, determining the extension and retraction of the legs based on the critical states of the two robot movements. Specifically, the method includes the following steps:

[0008] Step 1: Establish the robot's kinematic model:

[0009] The robot employs a design with 12 retractable legs, positioned along the central perpendicular lines of the 12 faces of a dodecahedron. This symmetrical leg distribution grants the robot omnidirectional mobility, allowing it to move from any posture in any direction, significantly reducing the complexity of motion planning. The robot's kinematic model is described by the following 13 physical quantities:

[0010] q=[xyzv x v y v z λ0λ1λ2λ3ω x ω y ω z ] T #(1)

[0011] Where [xyz] represents the coordinates of the robot's center of mass in the inertial frame, [v x v y v z [λ0λ1λ2λ3] represents the velocity of the center of mass in the inertial frame, [λ0λ1λ2λ3] represents the attitude of the machine in quaternion form, [ω] x ω y ω z ] represents the angular velocity in the body coordinate system.

[0012] Step 2: Calculate the contact forces acting on the robot and establish a dynamic model, as follows:

[0013] 2.1) Calculate the normal contact force acting on the robot.

[0014] This patent selects a linear spring-damped model to calculate the contact forces during contact, collision, relative sliding, and separation between the robot's foot and the ground. This method uses spring-damped parameters to describe the normal and tangential contact between objects.

[0015] F k =Kδ n #(2)

[0016]

[0017] Where K is the linear stiffness coefficient, D is the contact damping coefficient, and δ n The embedment depth of the robot's ground-touching foot. The embedding speed of the robot's ground-touching foot.

[0018] Therefore, the normal contact force acting on the robot is calculated as follows:

[0019]

[0020] 2.2) Calculate the tangential frictional force acting on the robot.

[0021] When calculating tangential friction, the relative tangential motion between the robot's foot and the ground is considered. Therefore, the tangential friction is:

[0022]

[0023] Where, δ s For the tangential relative sliding of the robot's ground-touching foot and the ground, The tangential relative velocity between the robot's ground-touching foot and the ground.

[0024] When F s When the maximum tangential frictional force is reached, plastic slip will occur at the contact surface. The condition for plastic slip to occur is determined by the friction coefficient μ. s and normal contact force F n Given: The complete tangential friction force can be expressed as:

[0025]

[0026] 2.3) Therefore, the total contact force acting on the robot is:

[0027]

[0028] 2.4) Obtain the dynamic model of the robot and calculate the resultant force of gravity and contact force acting on the robot:

[0029] F=mg+F1#(8)

[0030] The calculated contact torque is:

[0031]

[0032] In the formula, c is the distance from the robot's center to its leg, and δ n Embedment depth of the robot's ground-touching foot

[0033] The net torque acting on the robot is:

[0034]

[0035] In the formula, M T For the resultant torque, This is the gravitational torque.

[0036] Using the forces and torques described above, along with the robot's kinematic model, we can calculate the robot's next state. Differentiating the position, velocity, quaternion, and angular velocity in the kinematic model yields:

[0037]

[0038]

[0039]

[0040]

[0041] In the formula, [v x v y v z ] T For the robot's three components of velocity, [F] x F y F z ] T For the forces acting on the robot's three components, [a x a y a z ] T Let be the three components of the robot's acceleration. For the robot's three shared angular velocities, [α] x α y α z ] T Let λ0, λ1, λ2, and λ3 be the angular accelerations of the robot's three components, and let λ0, λ1, λ2, and λ3 be quaternions representing the robot's posture. Adding a "." above each character indicates that it represents the derivative of the physical quantity that character represents.

[0042] Therefore, the dynamic model of the robot is obtained:

[0043]

[0044] The above formula is used to adjust the robot's posture and control its motion.

[0045] Step 3: Determine the robot's direction of motion based on its real-time movement.

[0046] To plan the direction of motion for the robot at different positions along a predetermined path, this invention designs two methods for determining the direction of motion:

[0047] 3.1) First, we need to obtain two vectors: the perpendicular vector and the tangential vector.

[0048] When the robot moves along a predetermined path, it finds the point on the path closest to the robot. The perpendicular vector is the vector connecting the robot's center to this point, approximately perpendicular to the predetermined path, and its magnitude is approximately equal to the minimum distance from the robot to the predetermined path. The tangential vector is the vector in the tangential direction at this point. Simulation experiments have shown that when the tangential vector is 10% of the unit vector, the error is smaller. The perpendicular and tangential vectors determine the robot's direction of motion. The maximum observed error based on the motion direction determined by the above perpendicular and tangential vectors is the maximum predicted error. The preset initial distance mentioned below is related to the control tangential vector, therefore it refers to 10% of the unit vector, which is 0.1m.

[0049] When the robot's center position is inside the predetermined path, the perpendicular vector and tangential vector are determined. When the robot's center position is far from the predetermined path, the perpendicular direction dominates, as shown in formula (16). When the robot's center position is close to the predetermined path, the tangential direction dominates, as shown in formula (17). Specifically:

[0050] When the robot's center position is far from the predetermined path, the robot's direction of motion depends only on the vertical direction:

[0051]

[0052] When the robot's center position is close to the predetermined path:

[0053]

[0054] Where d = -AX + B is the tangential parameter, where... As control parameters, A controls the magnitude of the tangential vector, d0 is the preset initial distance, and δ max Let X be the length of the perpendicular line and B = d0, representing the maximum prediction error. X is the length of the perpendicular line, which is also the distance from the robot to the predetermined path, i.e., the motion error. X can influence the magnitude of d, thus allowing the robot's motion direction to be adjusted based on the motion error.

[0055] 3.2) First, two vectors are obtained: the perpendicular vector and the intercept vector. When the robot moves along the predetermined path, the point closest to the robot on the path is found, and the perpendicular vector is the same as described above. Then, a point a certain distance away from this point is found ahead on the path, and the line connecting the two points determines the intercept vector. Simulation experiments have shown that a distance of 0.1m is suitable. The perpendicular vector and the intercept vector determine the robot's direction of motion.

[0056] When the robot's center position is outside the predetermined path, the direction of motion is determined by formula (18). The magnitude of the intercept vector is related to the curvature of the predetermined path; the magnitude of the perpendicular vector is approximately equal to the minimum length of the robot to the predetermined path.

[0057]

[0058] Where d is related to the curvature of the path, the greater the curvature, the smaller the value of d; the smaller the curvature, the larger the value of d, and the smoother the motion at the inflection point. The expression for d is shown in formula (19):

[0059]

[0060] in, α is an empirical coefficient, taken as 0.1, ρ max Let ρ be the maximum curvature, ε be the curvature, B be the step size, and d0 be the preset initial distance. As the robot moves along the path, the point closest to the robot on the path changes at each step, thus the curvature ρ also changes. The curvature affects the parameter d1, thereby adjusting the robot's direction of motion in real time.

[0061] 3.3) Determine the robot's direction of motion:

[0062]

[0063] Step 4: Determine the extension and retraction of the robot's legs by observing two critical states of the robot's movement.

[0064] The robot, placed on a horizontal surface, has three retractable legs touching the ground. The extension and retraction of the legs are determined by two critical states of the robot's movement:

[0065] The first critical state determines when the forward telescopic leg begins to shorten. This first critical state refers to the situation where, with three telescopic legs touching the ground, one leg is at its longest while the other two are at their shortest, the projection of the robot's center of gravity onto the horizontal plane must shift out of the triangle formed by the three legs. Assuming that two of the three legs below the robot are at their shortest and one is at its longest, record the angle between the longest leg and the horizontal plane. This angle is α, the angle at which the forward telescopic leg begins to contact the ground. When α is 22.7°, the forward leg should shorten.

[0066] The second critical state determines when the rear retractable legs begin to extend. The second critical state refers to the situation where the robot, placed on a horizontal surface, has three retractable legs touching the ground. When all three legs touching the ground are in their shortest position, the angle β between the plane formed by the two rear legs and the horizontal plane is recorded. When β is 69°, the rear legs should extend.

[0067] The beneficial effects of this invention are as follows:

[0068] This invention enables real-time and effective control of the robot based on its center position, and adjusts the motion direction based on feedback from the overall error. By incorporating the curvature of the path into the motion planning, and adjusting the motion direction according to different path curvatures, the robot achieves lower errors when tracking complex paths. Attached Figure Description

[0069] Figure 1 This is a flowchart of a path tracking method for a spherical multi-extended legged robot according to the present invention;

[0070] Figure 2 This is a schematic diagram illustrating the determination of the direction of motion in the method of the present invention;

[0071] Figure 3 This is a schematic diagram illustrating the determination of leg extension and retraction in the method of the present invention. Detailed Implementation

[0072] The path tracking method of a spherical multi-extended legged robot of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0073] Example 1: As Figure 1 As shown, a path tracking method for a spherical multi-legged robot includes the following steps: establishing a dynamic model of the robot, obtaining the task path, determining the robot's center position; if it is on the inner side, controlling the direction of movement using perpendicular lines and tangents; if it is on the outer side, calculating the path curvature and controlling the direction of movement using perpendicular lines and tangents. Determining leg extension and retraction, the robot moves and repeats the above steps.

[0074] Example 2: Figure 2As shown, two vectors are first needed: a perpendicular vector and a tangential vector. When the robot moves along the predetermined path, the point closest to the robot on the path is found. The perpendicular vector is the vector connecting the robot's center to this point, approximately perpendicular to the predetermined path, and its magnitude is approximately equal to the minimum distance from the robot to the predetermined path. The tangential vector is the vector pointing tangentially to this point. Simulation experiments have shown that when the tangential vector is 10% of the unit vector, the error is smaller. The perpendicular and tangential vectors determine the robot's direction of motion. The maximum observed error based on the motion direction determined by the perpendicular and tangential vectors is the maximum predicted error. The preset initial distance mentioned below is related to the control tangential vector, therefore it refers to 10% of the unit vector, which is 0.1m.

[0075] Determining the direction of motion requires real-time assessment of the robot's center position. If the robot's center position is inside the path, the perpendicular and tangential vectors are determined. When the robot's center position is far from the predetermined path, the perpendicular direction dominates. Conversely, when the robot's center position is close to the predetermined path, the tangential direction dominates. Specifically:

[0076] When the robot's center position is far from the predetermined path, if the robot's center position is about 0.1m away from the path, the robot is far from the path, and the robot's direction of movement is only related to the vertical direction.

[0077]

[0078] When the robot's center position is close to the predetermined path, if the robot's center position is about 0.02m away from the path, the robot is relatively close to the path, and the robot's direction of motion is related to the tangent and perpendicular directions:

[0079]

[0080] Where d = -AX + B is the tangential parameter, d0 is the preset distance, δ max Let X be the length of the perpendicular line and B = d0, representing the maximum prediction error. If the preset distance is 0.1m and the maximum prediction error is 0.08m, then the closer the error is to 0.08m, the greater the proportion of the perpendicular vector in the direction of motion, and the faster the robot can return to the path; the closer the error is to 0, the greater the proportion of the tangential vector in the direction of motion, and the better the robot can move along the path.

[0081] When the robot's center position is outside the path, two vectors are first obtained: the perpendicular vector and the intercept vector. As the robot moves along the predetermined path, the point closest to the robot on the path is found, and the perpendicular vector is the same as described above. A point a certain distance away from this point is found ahead on the path, and the line connecting the two points determines the intercept vector. Simulation experiments have shown that a distance of 0.1m is suitable. The perpendicular and intercept vectors determine the robot's direction of motion.

[0082] When the robot's center position is outside the predetermined path, the direction of motion is determined by the tangential vector and the transverse vector. The magnitude of the transverse vector is related to the curvature of the predetermined path; the magnitude of the perpendicular vector is approximately equal to the minimum length of the robot to the predetermined path.

[0083]

[0084] The value of d is related to the curvature of the path. The greater the curvature, the smaller the value of d; the smaller the curvature, the larger the value of d, and the smoother the motion at the inflection point.

[0085]

[0086] in α is an empirical coefficient, taken as 0.1, ρ max Let ρ be the maximum curvature, ε be the curvature, B be the step size, and d0 be the preset initial distance. When the robot moves to a turn, the curvature is larger at the turn, and the perpendicular vector in the direction of movement has a larger proportion, so the robot can move close to the turn and will not deviate from the path. When the robot moves to a straight line, the curvature is smaller at the straight line, and the tangent vector in the direction of movement has a larger proportion, so the robot can move along the path better.

[0087] Therefore, the robot's direction of motion is determined:

[0088]

[0089] Example 3: As Figure 3 As shown, the extension and retraction of the legs are determined by two critical states. A robot placed on a horizontal surface has three extendable legs touching the ground. The first critical state determines when the front extendable leg begins to shorten. Assuming that two of the three legs touching the ground are at their shortest length and one is at its longest length, the angle between the longest leg and the horizontal plane is recorded. This angle is α, the angle at which the front extended leg begins to contact the ground. When α is 22.7°, the front leg should shorten. The second critical state determines when the rear extendable leg begins to extend. When all three legs touching the ground are at their shortest length, the angle β between the plane formed by the two rear legs and the horizontal plane is recorded. When β is 69°, the rear leg should extend.

[0090] Matters not covered in this invention are common knowledge.

[0091] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A path tracking method for a spherical multi-stretchable legged robot, characterized in that, Includes the following steps: First, establish the kinematic model of the robot; Secondly, calculate the contact forces acting on the robot and establish a dynamic model. Thirdly, based on the robot's real-time motion, design two methods to determine the motion direction: if the robot is inside the path, determine the motion direction using the tangent and perpendicular directions related to the path; if the robot is outside the path, determine the motion direction using the tangent and intercept directions related to the path. Finally, determine the extension and retraction of the legs based on the critical states of the two robot movements. Specifically, this includes the following steps: Step 1: Establish the robot's kinematic model: The robot employs a design with 12 retractable legs, positioned along the central perpendicular lines of the 12 faces of a dodecahedron. The robot's kinematic model is then described by the following 13 physical quantities: in, This represents the coordinates of the robot's center of mass in an inertial frame. This represents the velocity of the center of mass in an inertial frame of reference. The machine's posture is represented using quaternions. Represents the angular velocity in the body coordinate system; Step 2: Calculate the contact forces acting on the robot and establish a dynamic model, as follows: 2.1) Calculate the normal contact force acting on the robot. Using a linear spring-damping model, the contact forces during contact, collision, relative sliding, and separation between the robot's foot and the ground are calculated, yielding the normal contact force acting on the robot as follows: in, The linear stiffness coefficient is... The contact damping coefficient is... The embedment depth of the robot's ground-touching foot. The embedding speed of the robot's ground-touching foot; 2.2) Calculate the tangential frictional force acting on the robot. When calculating tangential friction, the relative tangential motion between the robot's foot and the ground is considered; therefore, the tangential friction is: in, For the tangential relative sliding of the robot's ground-touching foot and the ground, The tangential relative velocity between the robot's ground-touching foot and the ground; when When the maximum tangential frictional force is reached, plastic slip will occur at the contact surface. The condition for plastic slip to occur is determined by the coefficient of friction. and normal contact force The complete tangential friction force is given as: 2.3) The total contact force acting on the robot is: 2.4) Obtain the dynamic model of the robot. The resultant force of gravity and contact force acting on the robot is: The calculated contact torque is: In the formula, The distance from the robot's center to its legs. The embedding depth of the robot's ground-touching foot; The net torque acting on the robot is: In the formula, For the resultant torque, This is the gravitational torque; The resulting dynamic model of the robot is as follows: In the formula, The robot's velocity consists of three components. Let be the derivative of the quaternion, representing the robot's pose. Let be the three components of the robot's acceleration. Let be the angular acceleration of the robot in three components; The robot's posture is adjusted and motion is controlled by formula (15); Step 3: Determine the robot's direction of motion based on its real-time movements; For different positions of the robot on a predetermined path, different planning schemes are adopted to plan the direction of movement. Two methods for determining the direction of movement are designed: 3.1) First, determine the perpendicular vector and tangential vector; when the robot moves along the predetermined path, find the point on the path closest to the robot. The perpendicular vector is the vector of the line connecting the robot's center and this point, and the tangential vector is the vector of the tangential direction of this point; the perpendicular vector and tangential vector determine the robot's direction of motion; the maximum error observed is the maximum error predicted when the direction of motion is determined according to the above perpendicular vector and tangential vector. 3.2) First, obtain two vectors: the perpendicular vector and the intercept vector. When the robot moves along the predetermined path, find the point on the path closest to the robot. The perpendicular vector is the vector of the line connecting the robot's center and that point. Find a point a certain distance away from that point ahead on the path. The line connecting the two points determines the intercept vector. The perpendicular vector and the intercept vector determine the robot's direction of motion. 3.3) The robot's direction of motion is determined by the two methods in steps 3.1) and 3.2): Step 4: Determine the extension and retraction of the robot's legs by observing two critical states of the robot's movement; The robot, placed on a horizontal surface, has three retractable legs touching the ground. The extension and retraction of the legs are determined by two critical states of the robot's movement: The first critical state determines when the forward telescopic leg begins to shorten. This first critical state refers to a situation where, on a horizontal surface, three of the robot's telescopic legs are in contact with the ground. When one leg is at its longest and the other two are at their shortest, the projection of the robot's center of gravity onto the horizontal surface must move out of the triangle formed by the three legs. Assuming that two of the three legs below the robot are at their shortest and one is at its longest, record the angle between the longest leg and the horizontal surface. This angle represents the angle at which the forward telescopic leg begins to contact the ground. , When the angle is 22.7°, the foreleg shortens; The second critical state determines when the rear retractable legs begin to extend; the second critical state refers to the situation where, when the robot is placed on a horizontal surface, all three retractable legs are in contact with the ground, and all three legs are in their shortest position, the angle between the plane formed by the two rear legs and the horizontal plane is recorded. , The rear leg extends at a angle of 69°.

2. The path tracking method for a spherical multi-legged robot according to claim 1, characterized in that, in step 3.1), the perpendicular vector and tangential vector determine the robot's motion direction in the following way: When the robot's center position is inside the predetermined path, the above method is used to determine the perpendicular vector and the tangential vector; when the robot's center position is far from the predetermined path, the perpendicular direction dominates, as shown in formula (16); when the robot's center position is close to the predetermined path, the tangential direction dominates, as shown in formula (17). in, Let be the tangential parameter, where , as a control parameter, through Controlling the magnitude of the tangential vector, To preset the initial distance, The maximum error of the prediction, The vertical length is also the distance from the robot to the predetermined path, representing the motion error. It can affect The size of the value can be used to adjust the robot's direction of motion based on motion errors.

3. The path tracking method for a spherical multi-extended legged robot according to claim 1, characterized in that, In step 3.2), the specified distance is 0.1m.

4. The path tracking method for a spherical multi-stretchable robot according to claim 1, characterized in that, In step 3.2), the perpendicular vector and the intercept vector determine the robot's direction of motion as follows: When the robot's center position is outside the predetermined path, the direction of motion is determined by formula (18); the magnitude of the intercept vector is related to the curvature of the predetermined path; the magnitude of the perpendicular vector is approximately equal to the minimum length of the robot to the predetermined path. in, It is related to the curvature of the path; the greater the curvature, The smaller the value, the smaller the curvature. The larger the value, the smoother the movement at the inflection point; The expression is shown in formula (17): in, , This is an empirical coefficient. The maximum curvature, For curvature, It is a non-zero local minimum. Step size, Preset initial distance; parameters affected by curvature This allows for real-time adjustment of the robot's movement direction.

5. The path tracking method for a spherical multi-stretchable robot according to claim 4, characterized in that, The empirical coefficient Take 0.1.

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