Foot robot foot-ground contact model construction method applied to muddy terrain

Abstract

The invention belongs to the technical field of foot action mechanics. The invention discloses a method for constructing a foot-ground contact model of a foot-type robot applied to muddy terrains, which can improve the movement stability of the foot-type robot under the muddy terrains, and specifically comprises the following steps of: firstly, connecting a Burgers model, a nonlinear viscoplasticity model and a nonlinear spring model in series according to the viscoplasticity, viscoelasticity, elasticity and plastic deformation characteristics of the muddy terrains; a discrete element model describing the deformation characteristics is obtained. Then, based on the Mohr-Coulomb theory in soil mechanics, considering the influence of the soil bulk density, the water content and the clay content change of the mud land on the soil cohesion from the perspective of soil mechanics, and proposing and establishing a relational expression between the soil bulk density, the water content and the clay content change and the viscosity coefficient in the mud land discrete element model; and finally, according to the magnitude and the change trend of the normal force and the tangential force of the foot end, the foot-ground contact process is divided into three stages of foot falling, foot lifting and separation, and the transition process from foot falling to foot lifting is set as an independent stage. Wherein the foot falling stage and the foot lifting stage are further subdivided into an elastic deformation stage and a plastic deformation stage according to the deformation form of the mud land. In different stages, models describing corresponding characteristics in the muddy ground discrete element model are applied to construct a foot ground contact model. According to the method, the modeling precision of the foot-ground contact model of the muddy terrain can be improved, so that the foot type robot has higher adaptability under the muddy terrain.

Description

Technical Field

[0001] The present invention belongs to the technical field of foot-ground interaction mechanics, and in particular relates to a method for constructing a foot-ground contact model of a foot-type robot applied to muddy terrain. Background Art

[0002] Legged robots need to work in soft, bumpy and muddy outdoor terrain when performing reconnaissance, mapping and rescue tasks. This type of unstructured terrain often causes the robot's feet to sink due to the low pressure-bearing capacity of the soil, making it impossible to continue moving.

[0003] In existing research, soft ground is analyzed as a continuous medium, which is still at the macroscopic level and lacks precision. The shape of the supporting surface and the ground contact area cannot be accurately described, the ground stress distribution cannot be determined, and the movement and force conditions of the foot end and ground particles cannot be analyzed.

[0004] In summary, the foot-ground contact model constructed by the traditional method is difficult to describe the characteristics of muddy terrain. The present invention proposes a method for constructing a foot-ground contact model of a foot-type robot applied to muddy terrain. The corresponding discrete element model is determined according to the deformation form of the foot-ground contact in the muddy terrain, and the relationship between the soil's own properties and the viscosity coefficient is established. Different movement stages are divided, and the contact model between the foot and the muddy terrain is established according to the terrain deformation form corresponding to different stages, which is helpful for the foot-type robot to move stably in the muddy terrain. Summary of the invention

[0005] The purpose of the present invention is to provide a method for constructing a foot-ground contact model of a legged robot applied to muddy terrain, which can solve the problem that traditional modeling methods cannot describe the characteristics of muddy terrain. By using a combination of discrete element models suitable for the deformation characteristics of mud, a relationship between mud properties and viscosity coefficients is established, and rules for classifying foot-ground contact stages are preset, the accuracy of the established foot-ground contact model in describing the characteristics of muddy terrain can be improved.

[0006] The solution adopted by the present invention to solve the above problems is: a method for constructing a foot-ground contact model of a foot-type robot applied to muddy terrain, and the specific implementation process of the method is:

[0007] Step 1: According to the characteristics of mud terrain, viscoplastic deformation, viscoelastic deformation, elastic deformation and plastic deformation are determined as the four main deformation forms of foot-ground contact in mud terrain. A discrete element model describing the characteristics of mud terrain is established according to the deformation forms. The Burgers model is used to describe elastic and viscoelastic deformations, the nonlinear viscoplastic model is used to describe plastic and viscoplastic deformations, and the nonlinear spring model is used to describe the instantaneous stress when the foot contacts the ground, lifts up after stepping on it, and completely separates. The three models are connected in series to obtain a discrete element model describing the characteristics of mud terrain.

[0008] Step 2: According to the influence of the change of soil properties on soil cohesion, the change trend is analyzed from the perspective of soil mechanics. Based on the Mohr-Coulomb theory of soil mechanics, the relationship between soil bulk density, water content, clay content and viscosity coefficient in the nonlinear viscoplastic model is established;

[0009] Step 3: Preset the classification rules for foot-ground contact stages, divide the foot-ground contact process into three stages: landing, lifting, and leaving, and construct foot-ground contact models respectively. According to the deformation type of mud terrain, the landing and lifting stages are further divided into two stages of elastic and plastic deformation. In addition, the transition process from landing to lifting is set as one stage, and the stress of the model describing the corresponding characteristics is applied to construct the foot-ground contact model in different stages;

[0010] Beneficial effects of the present invention: The method for constructing a foot-ground contact model of a legged robot applied to muddy terrain can realize the construction of a foot-ground contact model that can simulate the characteristics of muddy terrain, and can improve the stability and safety of the legged robot operating in muddy terrain. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 A schematic diagram of a flow chart of a method for constructing a foot-ground contact model of a legged robot applied to muddy terrain according to an embodiment of the present invention Figure 2 A discrete element model diagram describing mud characteristics according to an embodiment of the present invention DETAILED DESCRIPTION

[0011] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and examples.

[0012] An embodiment of the present invention is a method for constructing a foot-ground contact model of a foot-type robot applied to muddy terrain, which comprises the following steps:

[0013] Step 1: By analyzing the characteristics of mud terrain, it is determined that viscoplastic deformation, viscoelastic deformation, elastic deformation and plastic deformation are the four main deformation forms caused by the contact between the mud and the foot end. A discrete element model describing the characteristics of mud terrain is established based on the deformation form, and the Burgers model composed of the Maxwell model and the Kelvin model in series is used to describe the elastic and viscoelastic deformations.

[0014] Because the traditional Burgers model cannot describe the accelerated creep behavior of soil, and considering the nonlinear viscoplastic characteristics of mud terrain, a nonlinear viscoplastic model that can describe the accelerated creep behavior is introduced to describe plastic and viscoplastic deformation. The characteristic of this model is that it will not enter the plastic deformation stage when the yield limit state is not reached, and this model can be ignored when calculating stress; when the nonlinear viscoplastic body reaches the yield limit state, it enters the plastic deformation stage. At this time, the corresponding part of the friction resistance needs to be deducted to solve the stress in the model.

[0015] A nonlinear spring model with progressive linear characteristics is connected in series to describe the instantaneous stress when the foot contacts the ground, lifts up after stepping on it, and separates from it. The model can exhibit nonlinear characteristics at small deformations and tend to be linear at large deformations, thereby reducing the nonlinear effect in the stable state of the model and providing a smoother mechanical response.

[0016] The above three models are connected in series to form a complete discrete element model. Figure 2 To describe the discrete element model diagram of mud characteristics, the discrete element model stress-strain relationship is shown in formulas (1) and (2): Where: σ is the total stress of the model; ε1, σ1, E1 and η1 are the strain, stress, elastic modulus and viscosity coefficient of the Maxwell model; ε2, σ2, E2 and η2 are the strain, stress, elastic modulus and viscosity coefficient of the Kelvin model; ε3, σ3, σ s and η3 are the strain, stress, yield strength and viscosity coefficient of the nonlinear viscoplastic model, respectively; n is defined as the creep index, which is used to describe the speed of accelerated creep; H is the Heaviside function, when σ≤σ s When H(σ-σ s )=0, when σ>σ s When H(σ-σ s )=σ-σ s ; ε4, σ4, E3 and E4 are the strain, stress, instantaneous elastic modulus of the linear part and the instantaneous elastic modulus of the nonlinear part of the nonlinear spring model respectively.

[0017] Step 2: Under the same dry density and different moisture content, with the increase of clay content, cohesion shows an overall upward trend. With the increase of moisture content, cohesion first increases and then decreases; when the bulk density increases, cohesion tends to increase. Analyzing the above trend from the perspective of soil mechanics, when the moisture content is low, the water mainly fills the gaps between soil particles, increasing the adhesion and friction between particles and increasing cohesion, which can be described by linear terms. As the moisture content increases further, the water begins to form a water film, and the effect of further increasing the moisture content gradually weakens, and begins to lubricate the friction between particles. The changes in this stage can be described by the square term. When the moisture content is too high, the soil particles are completely covered by the water film, the friction is significantly reduced, and the cohesion begins to decrease. Therefore, a combination of linear terms and square terms is used to capture its downward trend.

[0018] Within a certain range, the effect of soil compaction on mechanical properties is linear. Higher bulk density means higher compactness, thereby enhancing the shear strength of the soil. Therefore, a linear term is used to describe the effect of bulk density on soil cohesion.

[0019] The increase in clay content will increase the number of fine particles in the soil. Fine particles can fill the pores between larger particles, enhance the cohesion of the soil, and thus increase the cohesion. In the low to medium range, the linear relationship is a good approximation. In summary, based on the Mohr-Coulomb theory in soil mechanics, the relationship between soil bulk density, water content, clay content and viscosity coefficient is established as shown in formula (3): Where: η is the viscosity coefficient; c is the cohesion of the soil; σ is the normal stress on the soil; is the internal friction angle of the soil; ρ is the soil bulk density; θ is the soil water content; λ is the clay content in the soil; a is the constant term of the soil bulk density; b is the constant term of the linear term of soil water content; d is the constant term of the quadratic term of soil water content; e is the constant term of the clay content in the soil.

[0020] Step 3: The foot-ground contact process is divided into three stages: landing, lifting and disengagement. The landing and lifting stages are further divided into two stages: elastic deformation and plastic deformation according to the deformation type of the mud. In addition, the transition process from landing to lifting is set as an independent stage. Models describing corresponding characteristics are applied to construct the foot-ground contact model in different stages. The specific implementation is as follows:

[0021] The present invention designs a foot-ground contact model for a round-bottom rigid foot, which is divided into a normal contact model and a tangential contact model. The normal contact model describes the mechanical behavior of the foot end in the vertical direction, in which the normal force on the sole is provided by the normal stress of the sole and the shear stress on the side of the foot, while the tangential contact model studies the shear force on the horizontal plane, and the tangential force is provided by the shear stress of the sole.

[0022] The foot-ground contact process can be divided into three stages: landing, lifting and detachment according to the magnitude and changing trend of the normal force and tangential force at the foot end. The landing stage covers the process from the initial contact of the foot end to the complete contact with the ground, focusing on the gradual increase of contact impact and normal force to stability; the transition stage from landing to lifting describes the process from the foot end stepping on the muddy ground to lifting, at which time there are large instantaneous normal force and tangential force; the lifting stage describes the process from the foot end starting to lift off the ground to complete detachment, at which time the normal force gradually decreases, while the tangential force remains significant; the detachment stage marks that the foot end is completely off the ground and is no longer affected by any ground reaction force, the normal force disappears, and the tangential force gradually tends to zero.

[0023] According to the deformation type of mud terrain, the foot-ground contact model is subdivided into two stages: elastic deformation and plastic deformation during the foot placement and foot lift stages.

[0024] When establishing a foot-ground contact model, choosing a suitable model to calculate stress can accurately describe the mechanical properties and dynamic response of the terrain. Therefore, in the above-mentioned different stages, the stress of the model corresponding to the stage characteristics should be selected to establish the foot-ground contact model.

[0025] When the mud terrain undergoes elastic deformation during the landing phase, the normal force on the sole of the foot is mainly composed of Figure 2 The nonlinear spring model describing the instantaneous stress and the Maxwell model describing the elastic deformation stress are composed of the shear stress on the side of the foot calculated by the Janosi shear model, and the tangential force is only calculated by Figure 2 The stress components of the Maxwell model describing elastic deformation.

[0026] Therefore, the mud terrain undergoes elastic deformation during the landing phase, and the foot-ground normal contact model is shown in formula (4): In the formula, τ s is the shear stress of the interaction between the soil and the side wall of the foot end; r is the radius of the foot plantar; A is the surface area of ​​the foot plantar; S is the surface area of ​​the side of the foot; j is the tangential displacement of the foot end relative to the ground (m); K is the shear displacement modulus of the ground.

[0027] During the landing phase, the mud terrain undergoes elastic deformation and the foot-ground tangential contact model is shown in formula (5):

[0028] When the mud terrain undergoes plastic deformation during the landing phase, the normal force on the sole of the foot, the tangential force on the side of the foot, and the tangential force on the sole of the foot are all determined by Figure 2 Stress components of the nonlinear viscoplastic model describing plastic deformation.

[0029] Therefore, after the mud terrain undergoes plastic deformation during the landing phase, the normal contact model between the foot and the ground is as shown in formula (6):

[0030] During the footfall stage, the soil undergoes plastic deformation and the foot-ground tangential contact model is shown in formula (7):

[0031] In the transition phase from foot placement to foot lifting, the normal force and tangential force on the sole of the foot from stepping on the mud to lifting are Figure 2 The instantaneous stress of the nonlinear spring model is composed of Figure 2 The stress components provided by the Kelvin model describing the viscoelastic behavior.

[0032] Therefore, the foot-ground normal contact model in the transition stage from foot placement to foot lift is shown in formula (8):

[0033] Therefore, the foot-ground tangential contact model in the transition stage from foot landing to foot lifting can be obtained as shown in formula (9):

[0034] During the lifting phase, the mud terrain undergoes viscoelastic deformation, and the normal force on the sole, the tangential force on the side of the foot, and the tangential force on the sole are given by Figure 2 The stress components provided by the Kelvin model describing the viscoelastic behavior.

[0035] Therefore, the normal contact model of the foot and the ground during the foot lifting phase can be obtained as shown in formula (10):

[0036] During the foot-lifting stage, the mud terrain undergoes elastic deformation, and the foot-ground tangential contact model is shown in formula (11):

[0037] The soil undergoes plastic deformation during the lifting phase, and the normal and tangential foot-ground contact models are consistent with the foot-ground contact models of the mud terrain undergoing plastic deformation during the landing phase.

[0038] During the breakaway phase, the muddy terrain deforms under high stress, so the normal force and tangential force on the sole of the foot are only Figure 2 The instantaneous stress composition of the nonlinear spring model, the tangential force on the foot side is neglected.

[0039] Therefore, the normal contact model of the foot and the ground during the separation phase can be obtained as shown in formula (12):

[0040] The foot-ground tangential contact model during the separation phase is shown in formula (13):

[0041] The muddy ground foot-to-ground contact model constructed by the present invention can realize the method described in claim 1. The foot-to-ground contact model can describe the deformation characteristics of muddy ground terrain, and improve the viscosity coefficient according to soil properties, thereby improving the operating ability of the foot-type robot in muddy environments.

Claims

1. A method for constructing a foot-ground contact model of a foot-type robot applied to muddy terrain, characterized in that: The method comprises: A discrete element model is established to describe the characteristics of mud terrain, and the relationship between the soil bulk density, water content, clay content and the viscosity coefficient in the nonlinear viscoplastic model is constructed. The foot-ground contact model is established by pre-setting the rules for classifying the foot-ground contact stages.

2. The method according to claim 1, characterized in that A discrete element model is established to describe the characteristics of mud terrain, including: According to the characteristics of mud terrain, viscoplastic deformation, viscoelastic deformation, elastic deformation and plastic deformation are determined as the four main deformation forms of mud terrain contacting the foot end. The Burgers model is used to describe elastic and viscoelastic deformations, the nonlinear viscoplastic model is used to describe plastic and viscoplastic deformations, and the nonlinear spring model is used to describe the instantaneous stress when the foot contacts the ground, lifts up after stepping on it, and completely leaves it. The three models are connected in series to obtain a discrete element model that describes the characteristics of mud terrain. The stress-strain relationship of the discrete element model is shown in formulas (1) and (2): Where: σ is the total stress of the model; ε is the total strain of the model; σ1, ε1, E1, η1 are the stress, strain, elastic modulus and viscosity coefficient of the Maxwell model in the Burgers model; σ2, ε2, E2, η2 are the stress, strain, elastic modulus and viscosity coefficient of the Kelvin model in the Burgers model; ε3, σ3, σ s and η3 are the strain, stress, yield strength and viscosity coefficient of the nonlinear viscoplastic model, respectively; n is defined as the creep index, which is used to describe the speed of accelerated creep; H is the Heaviside function, when σ≤σ s When H(σ-σ s )=0, when σ>σ s When H(σ-σ s )=σ-σ s ; ε4, σ4, E3 and E4 are the strain, stress, instantaneous elastic modulus of the linear part and the instantaneous elastic modulus of the nonlinear part of the nonlinear spring model respectively.

3. The method according to claim 1, characterized in that Construct the relationship between soil bulk density, water content, clay content and viscosity coefficient in the nonlinear viscoplastic model, including: According to the influence of changes in soil bulk density, water content, and clay content on soil cohesion, the change trend is analyzed from the perspective of soil mechanics. The influence of bulk density and clay content on cohesion is expressed by linear terms, while the influence of water content on cohesion is expressed by a combination of linear terms and square terms. The relationship between soil bulk density, water content, clay content and the viscosity coefficient in the nonlinear viscoplastic model is established as shown in formula (3): Where: η is the viscosity coefficient; c is the cohesion of the soil; σ is the normal stress on the soil; is the internal friction angle of the soil; ρ is the soil bulk density; θ is the soil water content; λ is the clay content in the soil; a is the constant term of the soil bulk density; b is the constant term of the linear term of soil water content; d is the constant term of the quadratic term of soil water content; e is the constant term of the clay content in the soil.

4. The method according to claim 1, characterized in that The foot-ground contact model is established by pre-setting the classification foot-ground contact phase rules, including: According to the magnitude and changing trend of the normal force and tangential force at the foot end, the foot-ground contact process can be divided into three stages: landing, lifting, and separation. The transition process from landing to lifting is an independent stage. The landing stage includes the process from the initial contact of the foot end to the complete contact with the ground, focusing on the gradual increase of contact impact and normal force until stability; the lifting stage describes the process from the beginning of the foot lifting off the ground to the complete separation, at which time the normal force gradually decreases, while the tangential force is still significant; the separation stage marks that the foot end completely leaves the ground and is no longer affected by the ground reaction force, the normal force disappears, and the tangential force gradually tends to zero. The transition stage from landing to lifting involves the process from the foot end stepping on the mud to lifting, at which time the normal force and tangential force are instantaneously large. In the landing and lifting stages, according to the deformation form of the mud, it can be further divided into two stages: elastic deformation and plastic deformation. Models with different characteristics are used in different stages to construct the foot-ground contact model. The mud discrete element model, viscosity coefficient relationship, and foot-ground contact stage classification rules constructed by the present invention can realize the method described in claim 1, establish a foot-ground contact model for mud terrain, and improve the stability of the foot-type robot operating in mud terrain.

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