A statics modeling and control method and system for an underwater flexible robot arm

Abstract

This invention discloses a static modeling and control method and system for an underwater flexible manipulator. The underwater flexible manipulator includes a soft manipulator with a first flow channel, a second flow channel, and wiring holes inside. The static modeling and control method and system establish a static model of the soft manipulator considering the influence of deep-sea environmental pressure, which can be used to evaluate the driving pressure required by the soft manipulator at different water depths. An equivalent dynamic model of the soft manipulator is performed using an RPRP (rotation-translation-rotation-translation) rigid manipulator configuration, taking into account the change of the center of mass of the soft manipulator during the movement process, while reducing the model dimension and improving the computational efficiency of the dynamic controller. A series soft manipulator end-effector trajectory control method based on the dynamic model is proposed, which can accurately control the end effector according to the desired (generalized) angle, angular velocity, and angular acceleration.

Description

Technical Field

[0001] This invention relates to the fields of mechanics and control technology, specifically to a static modeling and control method and system for an underwater flexible robotic arm. Background Technology

[0002] Currently, soft actuators, as the basic unit of flexible actuators, have the advantages of fast response speed and strong shape adaptability, and are gradually being applied in fields such as industrial production lines, medical simulation research, and robotics. With the continuous advancement of the national deep-sea exploration strategy, soft actuators are beginning to shift towards underwater working scenarios, such as the recovery of underwater cultural relics. Patent document CN215848227U discloses a bionic soft manipulator that can be mounted on an underwater robot, providing a possibility for the underwater application of soft manipulators. Patent document CN112428298A discloses a soft manipulator and its control system, capable of generating unlimited degrees of freedom of movement, applicable to geological exploration and underwater search and rescue.

[0003] However, none of the above solutions explain how to precisely control the soft robotic arm underwater. According to existing technology, the difficulties in controlling underwater soft robotic arms are: First, soft robotic arms are continuum robots, and their models have high-order degrees of freedom, making them difficult to use for dynamic control; second, the posture of the soft robotic arm underwater is affected by environmental pressure, making it difficult to directly transplant empirical control methods from land (calibrating the bending angle and driving pressure of the flexible arm), and the models obtained by empirical methods lack clear physical meaning and cannot continue to be applied under external forces; furthermore, although the working state of the soft robotic arm can be predicted by real-time detection of the end effector posture through sensors, the manufacturing process and fiber confinement layer winding method prevent the soft robotic arm from performing pure bending motion, often involving some torsion. This poses a significant challenge to posture sensor-based feedback control tasks, while vision-based feedback control methods are often affected by factors such as water quality and lighting, lacking robustness and only serving as an auxiliary decision-making tool. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a static modeling and control method and system for an underwater flexible robotic arm, which can be used in different water depth environments.

[0005] To achieve the above objectives, the present invention adopts the following technical solution.

[0006] In some embodiments, a static modeling method for an underwater flexible manipulator is provided. The underwater flexible manipulator includes a soft manipulator, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft manipulator. The first and second flow channels are distributed on both sides of the wiring hole. The first and second flow channels are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft manipulator is externally constrained by reinforcing fibers and is cylindrical in shape.

[0007] In an underwater environment, when the underwater flexible robotic arm is driven, the first and second channels are filled with liquid, and the first and second channels have a first channel pressure P1 and a second channel pressure P2, respectively. The first channel pressure P1 is less than or equal to the second channel pressure P2. The first and second channels are bent, with the first channel being a bent short-side channel and the second channel being a bent long-side channel. The side of the flexible robotic arm closest to the first channel is the bent short-side, and the side of the flexible robotic arm closest to the second channel is the bent long-side.

[0008] The static modeling method for the underwater flexible robotic arm includes:

[0009] Simultaneously, the radial force balance, circumferential force balance, and axial force balance along the soft manipulator cross-section of the underwater flexible manipulator are modeled to generate a static model of the underwater flexible manipulator. The static model of the underwater flexible manipulator includes a radial force balance model, a circumferential force balance model, and an axial force balance model. The outer periphery of the cross-section of the soft manipulator is circular.

[0010] The radial force balance model includes a radial force balance model for a curved short-side channel and a radial force balance model for a curved long-side channel.

[0011] The radial force balance model for the curved short-side flow channel is as follows:

[0012]

[0013] P1f h (r 11 ,α1)f H (λ+r 11 )=P0f H (λ+d1 / 2)d1+k1Δr 11 ,

[0014] Where P0 is the underwater environmental pressure, D is the outer diameter of the soft robotic arm, k1 and k2 are the equivalent stiffness coefficients on the side near the center and the side near the outer edge of the cross-section of the soft robotic arm, respectively, and d1 represents the equivalent diameter of the wiring hole of the soft robotic arm on the curved short side after the flow channel is filled with liquid.

[0015] r 11 r 12 Δr represents the radius of the inner side and the outer side of the curved short-side flow channel after filling with liquid. 11 and Δr 12 This indicates the change in the radius of the inner side and outer side of the curved short-side flow channel after filling with liquid, relative to the radius when not filled with liquid.

[0016] λ is the equivalent bending radius of the neutral layer after the soft robotic arm bends, which is related to the elongation of the soft robotic arm on both sides in the bending plane;

[0017] α i (i = 1, 2) represents the central angle of the arc length of the first and second flow channels on the cross-section after filling with liquid, where i = 1 represents the curved short side flow channel and i = 2 represents the curved long side flow channel;

[0018] f h (·) represents the arc length function of the force-bearing surfaces of the first and second flow channels on the cross-section, f h (r,α)=rα;

[0019] f H (·) represents the arc length function along the axis of the soft robotic arm.

[0020]

[0021] Where Δl1 represents the bending short-side elongation of the soft robotic arm, and Δl2 represents the bending long-side elongation of the soft robotic arm.

[0022] The radial force balance model for the curved long side channel is as follows:

[0023]

[0024] P0f H (λ+d2 / 2)d2+k1Δr 21 =P2f h (r 21 ,α2)f H (λ+r 21 ),

[0025] In the above formula, d2 is the equivalent diameter of the wiring hole of the soft robotic arm on the long curved side after the flow channel is filled with liquid. 21 r 22 Δr represents the radius of the inner side and the outer side of the curved long side channel after filling with liquid. 21 and Δr 22 This indicates the change in radius of the inner side of the curved long side flow channel and the outer side of the curved short side flow channel after filling with liquid, relative to the radius when not filled with liquid;

[0026] The circumferential force balance model is as follows:

[0027]

[0028]

[0029] In the above formula, k3 is the equivalent stiffness coefficient of the soft robotic arm in the circumferential direction. and These represent the circumferential elongation of the flow channel after filling the curved short-side flow channel and the curved long-side flow channel, respectively. The calculation formulas are as follows:

[0030]

[0031]

[0032] Where Δα1 and Δα2 satisfy:

[0033] α² = 2Δα² + α

[0034] α1=2Δα1+α,

[0035] Where α is the original central angle corresponding to the first and second flow channels;

[0036] The axial force balance model is as follows:

[0037]

[0038]

[0039] In the above formula, k a S1 represents the equivalent stiffness coefficient of the soft manipulator in the axial direction, and S2 represents the effective area of ​​the soft manipulator against the underwater environmental pressure along the axial direction on the short and long sides of the bend, respectively. The calculation formula is as follows:

[0040]

[0041]

[0042] in,

[0043] d1=d-2Δr 11

[0044] d2=d-2Δr 21

[0045] In the above formula, d is the original diameter of the wiring hole of the soft robotic arm.

[0046] In some embodiments, the equivalent stiffness coefficient in the static model of the underwater flexible manipulator is a known quantity related to material properties and geometry, and the underwater environmental pressure, the pressure of the first flow channel, and the pressure of the second flow channel are collected by pressure sensors.

[0047] The bending elongation Δl2 and bending short elongation Δl1 of the soft robotic arm are obtained by solving the following formula: The bending angle θ of the soft robotic arm is obtained by solving the following formula:

[0048]

[0049] In some embodiments, a static modeling and control method for an underwater flexible manipulator is provided. The underwater flexible manipulator static modeling and control method includes the underwater flexible manipulator static modeling method described above, and further includes:

[0050] The soft robotic arm is equivalent to a rigid robotic arm model with a configuration of "rotation-translation-rotation-translation", and each joint is represented by the DH parameter method as follows:

[0051]

[0052] In the above formula, m i (·) represents the constraint that the position and orientation of the soft robotic arm's end effector are equivalently replaced by a rigid robotic arm model, where i represents the i-th joint of the soft robotic arm, and q i This represents the motion parameters of the i-th joint, which include angle and displacement;

[0053] The constraint equations for n soft robotic arms connected in series are:

[0054] m(q)=[m1(q1) T ...m n (q n ) T In some embodiments, n is a natural number greater than or equal to 2.

[0055] In some embodiments, the dynamic model of the soft robotic arm is calculated and defined as follows:

[0056] ξ = m(q),

[0057]

[0058]

[0059] In the above formula, J m (q) represents the Jacobian matrix, and the i-th term is calculated as follows:

[0060]

[0061] In some embodiments, the dynamic model equations of the soft robotic arm can be expressed as:

[0062]

[0063] In the above formula, f ex The vector represents the load-bearing capacity of the soft robotic arm, J represents the Jacobian matrix, and B, C, and D represent the load-bearing capacity of the soft robotic arm. V G, K, and G represent the inertia matrix, Coriolis force matrix, damping matrix, mass matrix, and stiffness matrix, respectively, with the joint motion parameters as variables. The calculation methods are as follows:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] In the above formula, B ξ C ξ G ξ Let β represent the inertia matrix, Coriolis force matrix, and mass matrix, respectively, with ξ as the variable. i E is the bending damping coefficient of the soft robotic arm. i I is the elastic modulus of the soft robotic arm. i Let be the moment of inertia of the soft robotic arm.

[0071] In some embodiments, the method includes:

[0072] The input torque τ is:

[0073]

[0074] In the above formula, Let represent the desired joint pose, velocity, and acceleration of the soft robotic arm, respectively; the first two terms on the right side of the equation represent the feedforward control terms; the joint acceleration of the soft robotic arm is calculated using the velocity:

[0075]

[0076] In the above formula, k represents the time step, and Δt represents the control period.

[0077] In some embodiments, an underwater flexible robotic arm control system is provided, the underwater flexible robotic arm control system including control according to the underwater flexible robotic arm static modeling and control method as described in any of the preceding claims.

[0078] Compared with the prior art, the beneficial effects of some embodiments of the present invention are at least as follows: (1) A static model of a soft manipulator considering the influence of deep-sea environmental pressure is established, which can be used to evaluate the driving pressure required by the soft manipulator at different water depths; (2) The soft manipulator is modeled in an equivalent dynamic manner by using the RPRP (rotation-translation-rotation-translation) rigid manipulator configuration, taking into account the change of the center of mass of the soft manipulator during the action process, while reducing the model dimension of the soft manipulator and improving the computational efficiency of the dynamic controller; (3) A series soft manipulator end trajectory control method based on the dynamic model is proposed, which can be accurately controlled according to the desired (generalized) angle, angular velocity and angular acceleration. Attached Figure Description

[0079] Figure 1 This is a schematic diagram of the cross-sectional geometry of a single soft robotic arm before and after driving, according to an embodiment of the present invention.

[0080] Figure 2 This is a schematic diagram of the equivalent configuration of a single soft robotic arm after bending in one embodiment of the present invention.

[0081] Figure 3 This is a schematic diagram of the control of a serial soft robotic arm in one embodiment of the present invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0083] In the description of this invention, it should be understood that the terms "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. The interpretation of such terms should be made from the perspective of a person skilled in the art. For example, "above" or "below" should be understood as the positional relationship of the main structure or structure of a component, etc., in its initial state, which may be broken during movement. "...set on" should be understood as the general connection relationship of the components, not necessarily above.

[0084] In this invention, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly from the perspective of someone skilled in the art. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0085] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0086] like Figure 1-3 As shown, some embodiments of this application provide a static modeling method for an underwater flexible manipulator. The underwater flexible manipulator includes a soft manipulator, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft manipulator. The first and second flow channels are distributed on both sides of the wiring hole. The first and second flow channels are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft manipulator is externally constrained by reinforcing fibers and is cylindrical in shape.

[0087] In an underwater environment, when the underwater flexible robotic arm is actuated, the first and second flow channels are filled with liquid. The first and second flow channels each have a first flow channel pressure P1 and a second flow channel pressure P2, respectively. The first flow channel pressure P1 is less than or equal to the second flow channel pressure P2. The first and second flow channels are curved, with the first flow channel being the curved short-side channel and the second flow channel being the curved long-side channel. The side of the flexible robotic arm closest to the first flow channel is the curved short-side, and the side closest to the second flow channel is the curved long-side. The side of the flexible robotic arm closest to the wiring hole is the inner side (near the center), and the side furthest from the wiring hole is the outer side (farthest from the center). In some embodiments, P1 is less than P2. It is understood that the positions of the first and second flow channels can be interchanged. This embodiment is for illustrative purposes only.

[0088] The static modeling method for the underwater flexible robotic arm includes:

[0089] Simultaneously, the radial force balance, circumferential force balance, and axial force balance along the cross-section of the soft manipulator of the underwater flexible manipulator are modeled to generate a static model of the underwater flexible manipulator. The static model of the underwater flexible manipulator includes a radial force balance model, a circumferential force balance model, and an axial force balance model. The outer periphery of the cross-section of the soft manipulator is circular.

[0090] In this embodiment, a static model of a single underwater flexible manipulator is performed, considering both radial and circumferential force balance on the cross-section of the soft manipulator and force balance along the axial direction of the soft manipulator, as shown in the attached figure. Figure 1 As shown, the soft robotic arm has two flow channels (shown in shaded areas in the figure), namely the first flow channel and the second flow channel. The cross-section of the flow channels is arc-shaped. The flow channels are used to fill with liquid to generate pressure. The pressure difference between the first flow channel and the second flow channel drives the movement of the underwater soft robotic arm.

[0091] The radial force balance model includes a radial force balance model for a curved short-side channel and a radial force balance model for a curved long-side channel.

[0092] The radial force balance model for the curved short-side flow channel is as follows:

[0093]

[0094] P1f h (r 11 ,α1)f H (λ+r 11 )=P0f H (λ+d1 / 2)d1+k1Δr 11 ,

[0095] Where P0 is the underwater environmental pressure, D is the outer diameter of the soft robotic arm, k1 and k2 are the equivalent stiffness coefficients on the side near the center and the side near the outer edge of the cross-section of the soft robotic arm, respectively, and d1 represents the equivalent diameter of the wiring hole of the soft robotic arm on the short side of the bend after the flow channel on the short side is filled with liquid. 11 r 12 Δr represents the radius of the inner side and the outer side of the curved short-side flow channel after filling with liquid. 11 and Δr 12 This indicates the change in the radius of the inner side and outer side of the curved short-side flow channel after filling with liquid, relative to the radius when not filled with liquid.

[0096] λ is the equivalent bending radius of the neutral layer after the soft robotic arm bends, which is related to the elongation of the soft robotic arm on both sides in the bending plane;

[0097] α i (i = 1, 2) represents the central angle of the arc length of the first and second flow channels on the cross-section after filling with liquid, where i = 1 represents the curved short side flow channel and i = 2 represents the curved long side flow channel;

[0098] f h (·) represents the arc length function of the force-bearing surfaces of the first and second flow channels on the cross-section, f h (r,α)=rα;

[0099] f H (·) represents the arc length function along the axis of the soft robotic arm.

[0100]

[0101] Where Δl1 represents the bending short-side elongation of the soft robotic arm, and Δl2 represents the bending long-side elongation of the soft robotic arm.

[0102] The radial force balance model for the curved long side channel is as follows:

[0103]

[0104] P0f H (λ+d2 / 2)d2+k1Δr 21 =P2f h (r 21 ,α2)f H (λ+r 21 ),

[0105] In the above formula, d2 is the equivalent diameter of the wiring hole of the soft robotic arm on the long curved side after the flow channel is filled with liquid, and r is the equivalent diameter of the flow channel on the long curved side. 21 r 22 Δr represents the radius of the inner side and the outer side of the curved long side channel after filling with liquid. 21 and Δr 22 This represents the change in radius of the inner side of the curved long-side flow channel and the outer side of the curved short-side flow channel after filling with liquid, relative to the radius when not filled with liquid. The radial force balance equation on the cross-section of the underwater soft manipulator simultaneously considers the curved long-side flow channel and the curved short-side flow channel. Each flow channel is divided into the inner side (near the center) and the outer side (far from the center).

[0106] The circumferential force balance model is as follows:

[0107]

[0108]

[0109] In the above formula, k3 is the equivalent stiffness coefficient of the soft robotic arm in the circumferential direction. and These represent the circumferential elongation of the flow channel after filling the curved short-side flow channel and the curved long-side flow channel, respectively. The calculation formulas are as follows:

[0110]

[0111]

[0112] Where Δα1 and Δα2 satisfy:

[0113] α² = 2Δα² + α

[0114] α1=2Δα1+α,

[0115] Where α is the original central angle corresponding to the first and second flow channels;

[0116] The axial force balance model is as follows:

[0117]

[0118]

[0119] In the above formula, k a S1 represents the equivalent stiffness coefficient of the soft manipulator in the axial direction, and S2 represents the effective area of ​​the soft manipulator against the underwater environmental pressure along the axial direction on the short and long sides of the bend, respectively. The calculation formula is as follows:

[0120]

[0121]

[0122] in,

[0123] d1=d-2Δr 11

[0124] d2=d-2Δr 21

[0125] In the above formula, d is the original diameter of the wiring hole of the soft robotic arm.

[0126] In some embodiments, the equivalent stiffness coefficient in the static model of the underwater flexible manipulator is a known quantity related to material properties and geometry. The underwater environmental pressure, the pressure in the first flow channel, and the pressure in the second flow channel are collected by pressure sensors. Combining the above equations, it can be seen that the static equations of the underwater single-unit soft manipulator system contain a total of 8 unknowns, namely Δr... 21 Δr 11 Δr 22 Δr 12Δα1, Δα2, Δl1, and Δl2. Therefore, the expressions for the elongation of the soft robotic arm on the long and short sides of the bend can be obtained, and thus the bending angle of the soft robotic arm can be obtained.

[0127] In some embodiments, the method further includes solving for the bending elongation Δl2 and bending short elongation Δl1 of the soft robotic arm, wherein the bending angle θ of the soft robotic arm is obtained by the following formula:

[0128]

[0129] In some embodiments, reference Figure 2 The underwater flexible manipulator static modeling and control method includes modeling according to the underwater flexible manipulator static modeling method described in any of the above embodiments, and further includes:

[0130] The soft robotic arm is equivalent to a rigid robotic arm model with a configuration of "rotation-translation-rotation-translation", and each joint is represented by the DH parameter method as follows:

[0131]

[0132] In the above formula, m i (·) represents the constraint that the position and orientation of the soft robotic arm's end effector are equivalently replaced by a rigid robotic arm model, where i represents the i-th joint of the soft robotic arm, and q i This represents the motion parameters of the i-th joint, including angle and displacement. In this embodiment, it can be assumed that the single soft manipulator is equivalent to a rigid body joint combination with a configuration of RPRP (rotation-translation-rotation-translation), and the constraints of the soft manipulator's end-effector position / center of mass and attitude are equivalently replaced by the rigid manipulator model. DH parameters (Denavit-Hartenberg parameters) are a mathematical model and coordinate system for determining the manipulator using four parameters to express the positional and angular relationship between two pairs of joint links.

[0133] In some embodiments, reference Figure 3 The underwater flexible manipulator static modeling and control method is a series soft manipulator end-effector trajectory control method based on a dynamic model. The series soft manipulator includes n soft manipulators, and the constraint equations for the n soft manipulators connected in series are:

[0134] m(q)=[m1(q1) T ...m n (q n ) T ], where n is a natural number greater than or equal to 2. It is understandable that...

[0135] In some embodiments, the method further includes: calculating a dynamic model of the soft robotic arm and defining it as follows:

[0136] ξ = m(q),

[0137]

[0138]

[0139] In the above formula, J m (q) represents the Jacobian matrix, and the i-th term is calculated as follows:

[0140] Where L i This represents the length of the i-th soft robotic arm.

[0141] In some embodiments, the dynamic model equations of the soft robotic arm can be expressed as:

[0142]

[0143] In the above formula, the left side represents the internal force acting on the soft robotic arm, and the right side represents the external force acting on the soft robotic arm. ex The vector represents the load-bearing capacity of the soft robotic arm, J represents the Jacobian matrix, and B, C, DV, G, and K represent the joint parameters q, q, and q respectively. The inertia matrix, Coriolis force matrix, damping matrix, mass matrix, and stiffness matrix, which are variables, are calculated as follows:

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150] In the above formula, B ξ C ξ G ξ Let β represent the inertia matrix, Coriolis force matrix, and mass matrix, respectively, with ξ as the variable. i E is the bending damping coefficient of the soft robotic arm. i I is the elastic modulus of the soft robotic arm. i Let be the moment of inertia of the soft robotic arm.

[0151] In some embodiments, the method includes: employing the following control method based on the above model:

[0152] The input torque τ is:

[0153]

[0154] In the above formula, Let represent the desired joint pose, velocity, and acceleration of the soft robotic arm, respectively; the first two terms on the right side of the equation represent the feedforward control terms.

[0155] In some embodiments, the joint acceleration of the soft robotic arm is calculated using velocity:

[0156]

[0157] In the above formula, k represents the time step, and Δt represents the control cycle. The joint acceleration of the soft robotic arm is calculated using velocity parameters, making the control speed changes of the soft robotic arm smoother.

[0158] In some embodiments, an underwater flexible robotic arm control system is also provided. The underwater flexible robotic arm includes a soft robotic arm, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft robotic arm. The first flow channel and the second flow channel are distributed on both sides of the wiring hole. The first flow channel and the second flow channel are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft robotic arm is reinforced with fiber constraints on the outside. The soft robotic arm is cylindrical.

[0159] The underwater flexible robotic arm control system includes control according to the underwater flexible robotic arm static modeling and control method as described in any of the above embodiments.

[0160] In some embodiments, an underwater flexible robotic arm control system is also provided. The underwater flexible robotic arm includes a soft robotic arm, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft robotic arm. The first flow channel and the second flow channel are distributed on both sides of the wiring hole. The first flow channel and the second flow channel are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft robotic arm is reinforced with fiber constraints on the outside. The soft robotic arm is cylindrical.

[0161] The underwater flexible robotic arm control system also includes modeling according to the underwater flexible robotic arm static modeling method described in any of the above.

[0162] It is understood that the above embodiments of this application establish a static model of the soft manipulator considering the influence of deep-sea environmental pressure, which can be used to evaluate the driving pressure required by the soft manipulator at different water depths. Some embodiments of this application perform equivalent dynamic modeling of the soft manipulator using an RPRP rigid body manipulator configuration, taking into account the change of the center of mass of the soft manipulator during the movement process, while reducing the dimensionality of the soft manipulator model and improving the computational efficiency of the dynamic controller. Some embodiments of this application also propose a series soft manipulator end-effector trajectory control method based on the dynamic model, which can accurately control the end effector according to the desired (generalized) angle, angular velocity, and angular acceleration.

[0163] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A static modeling method for an underwater flexible robotic arm, characterized in that, The underwater flexible robotic arm includes a soft robotic arm, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft robotic arm. The first and second flow channels are distributed on both sides of the wiring hole. The first and second flow channels are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft robotic arm is reinforced with fiber constraints on the outside and is cylindrical in shape. In an underwater environment, when the underwater flexible robotic arm is driven, the first and second channels are filled with liquid, and the first and second channels have a first channel pressure P1 and a second channel pressure P2, respectively. The first channel pressure P1 is less than or equal to the second channel pressure P2. The first and second channels are bent, with the first channel being a bent short-side channel and the second channel being a bent long-side channel. The side of the flexible robotic arm closest to the first channel is the bent short-side, and the side of the flexible robotic arm closest to the second channel is the bent long-side. The static modeling method for the underwater flexible robotic arm includes: Simultaneously, the radial force balance, circumferential force balance, and axial force balance along the soft manipulator cross-section of the underwater flexible manipulator are modeled to generate a static model of the underwater flexible manipulator. The static model of the underwater flexible manipulator includes a radial force balance model, a circumferential force balance model, and an axial force balance model. The outer periphery of the cross-section of the soft manipulator is circular. The radial force balance model includes a radial force balance model for a curved short-side channel and a radial force balance model for a curved long-side channel. The radial force balance model for the curved short-side flow channel is as follows: P1f h (r 11 ,a1)f H (λ+r 11 )=P0f H (λ+d1 / 2)d1+k1Δr 11 , Where P0 is the underwater environmental pressure, D is the outer diameter of the soft robotic arm, k1 and k2 are the equivalent stiffness coefficients on the side near the center and the side near the outer edge of the cross-section of the soft robotic arm, respectively, and d1 represents the equivalent diameter of the wiring hole of the soft robotic arm on the curved short side after the flow channel is filled with liquid. r 11 r 12 Δr represents the radius of the inner side and the outer side of the curved short-side flow channel after filling with liquid. 11 and Δr 12 This indicates the change in the radius of the inner side and outer side of the curved short-side flow channel after filling with liquid, relative to the radius when not filled with liquid. λ is the equivalent bending radius of the neutral layer after the soft robotic arm bends, which is related to the elongation of the soft robotic arm on both sides in the bending plane; α i (i = 1, 2) represents the central angle of the arc length of the first and second flow channels on the cross-section after filling with liquid, where i = 1 represents the curved short side flow channel and i = 2 represents the curved long side flow channel; f h (·) represents the arc length function of the force-bearing surfaces of the first and second flow channels on the cross-section. f h (r,α)＝rα； f H (·) represents the arc length function along the axis of the soft robotic arm. Where Δl1 represents the bending short-side elongation of the soft robotic arm, and Δl2 represents the bending long-side elongation of the soft robotic arm. The radial force balance model for the curved long side channel is as follows: P0f H (λ+d2 / 2)d2+k1Δr 21 =P2f h (r 21 ,α2)f H (λ+r 21 ), In the above formula, d2 is the equivalent diameter of the wiring hole of the soft robotic arm on the long curved side after the flow channel is filled with liquid, and r is the equivalent diameter of the flow channel on the long curved side. 21 r 22 Δr represents the radius of the inner side and the outer side of the curved long side channel after filling with liquid. 21 and Δr 22 This indicates the change in radius of the inner side of the curved long side flow channel and the outer side of the curved short side flow channel after filling with liquid, relative to the radius when not filled with liquid; The circumferential force balance model is as follows: In the above formula, k3 is the equivalent stiffness coefficient of the soft robotic arm in the circumferential direction. and These represent the circumferential elongation of the flow channel after filling the curved short-side flow channel and the curved long-side flow channel, respectively. The calculation formulas are as follows: Where Δα1 and Δα2 satisfy: α² = 2Δα² + α α1=2Δα1+α, Where α is the original central angle corresponding to the first and second flow channels; The axial force balance model is as follows: In the above formula, k a S1 represents the equivalent stiffness coefficient of the soft manipulator in the axial direction, and S2 represents the effective area of ​​the soft manipulator against the underwater environmental pressure along the axial direction on the short and long sides of the bend, respectively. The calculation formula is as follows: in, d1=d-2Δr 11 d2=d-2Δr 21 In the above formula, d is the original diameter of the wiring hole of the soft robotic arm.

2. The underwater flexible robotic arm static modeling method according to claim 1, characterized in that, The equivalent stiffness coefficient in the static model of the underwater flexible robotic arm is a known quantity related to material properties and geometry. The underwater environmental pressure, the pressure of the first flow channel, and the pressure of the second flow channel are collected by pressure sensors. The bending elongation Δl2 and bending short elongation Δl1 of the soft robotic arm are obtained by solving the following formula: The bending angle θ of the soft robotic arm is obtained by solving the following formula:

3. A method for static modeling and control of an underwater flexible robotic arm, characterized in that, The underwater flexible manipulator static modeling and control method includes the underwater flexible manipulator static modeling method according to claim 1 or 2, and further includes: The soft robotic arm is equivalent to a rigid robotic arm model with a configuration of "rotation-translation-rotation-translation", and each joint is represented by the DH parameter method as follows: In the above formula, m i (·) represents the constraint that the position and orientation of the soft robotic arm's end effector are equivalently replaced by a rigid robotic arm model, where i represents the i-th joint of the soft robotic arm, and q i L represents the motion parameters of the i-th joint, including angle and displacement. i This represents the length of the i-th soft robotic arm.

4. The underwater flexible robotic arm static modeling and control method according to claim 3, characterized in that, The static modeling and control method for the underwater flexible manipulator is a trajectory control method for the end effector of a series of soft manipulators based on a dynamic model. The series of soft manipulators includes n soft manipulators, and the constraint equations for the n soft manipulators connected in series are as follows: m(q)=[m1(q1) T ...m n (q n ) T ], where n is a natural number greater than or equal to 2.

5. The underwater flexible robotic arm static modeling and control method according to claim 4, characterized in that, Calculate the dynamic model of the soft robotic arm and define it as follows: ξ = m(q), In the above formula, J m (q) represents the Jacobian matrix, and the i-th term is calculated as follows:

6. The underwater flexible robotic arm static modeling and control method according to claim 5, characterized in that, The dynamic model equations of the soft robotic arm can be expressed as: In the above formula, the left side represents the internal force acting on the soft robotic arm, and the right side represents the external force acting on the soft robotic arm, f. ex The vector represents the load-bearing capacity of the soft robotic arm, J represents the Jacobian matrix, and B, C, and D represent the load-bearing capacity of the soft robotic arm. V G, K, and G represent the inertia matrix, Coriolis force matrix, damping matrix, mass matrix, and stiffness matrix, respectively, with the joint motion parameters as variables. The calculation methods are as follows: In the above formula, B ξ C ξ G ξ Let β represent the inertia matrix, Coriolis force matrix, and mass matrix, respectively, with ξ as the variable. i E is the bending damping coefficient of the soft robotic arm. i I is the elastic modulus of the soft robotic arm. i Let q be the moment of inertia of the soft robotic arm. These are the motion parameters of the joint.

7. The underwater flexible robotic arm static modeling and control method according to claim 6, characterized in that, The method includes: The input torque τ is: In the above formula, Let represent the desired joint pose, velocity, and acceleration of the soft robotic arm, respectively; the first two terms on the right side of the equation represent the feedforward control terms.

8. The underwater flexible robotic arm static modeling and control method according to claim 7, characterized in that, The joint acceleration of a soft robotic arm is calculated using velocity: In the above formula, k represents the time step, and Δt represents the control period.

9. A control system for an underwater flexible robotic arm, characterized in that, The underwater flexible robotic arm includes a soft robotic arm, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft robotic arm. The first and second flow channels are distributed on both sides of the wiring hole. The first and second flow channels are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft robotic arm is reinforced with fiber constraints on the outside and is cylindrical in shape. The underwater flexible robotic arm control system is controlled by the underwater flexible robotic arm static modeling and control method according to any one of claims 3-8.

10. A control system for an underwater flexible robotic arm, characterized in that, The underwater flexible robotic arm includes a soft robotic arm, which has a first flow channel, a second flow channel, and a wiring hole inside. The wiring hole is located at the center of the soft robotic arm. The first and second flow channels are distributed on both sides of the wiring hole. The first and second flow channels are arc-shaped flow channels. The wiring hole has a circular cross-section. The soft robotic arm is reinforced with fiber constraints on the outside and is cylindrical in shape. The underwater flexible robotic arm control system also includes modeling using the underwater flexible robotic arm static modeling method according to any one of claims 1-2.

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