Modeling Of Foot-terrain Interaction Mechanics With Application To Plantigrade Quadruped Robots In Design And Simulation

As a branch of contact mechanics,foot-terrain interaction mechanics for legged robots are of great significance in foot structure design,body motion simulation,trajectory planning,tracking control,and terrain environment parameter identification.The quasi-static contact modeling of hard ground is usually obtained by geometric motion constraints,and the dynamic contact is predicted by elastic collision or elastic-plastic model.However,the traditional contact model can't be used and specified researches are required on soft ground environment such as sand,frozen soil,tundra and extraterrestrial planet surface,because complex phenomena including normal sinkage and tangential slipping are generated on them.There are two kinds of contact forms between robot legs and soft ground:translation and rotation.The translational contact is the conventional contact form of particles,while the rotary contact mostly occurs between rigid or deformable bodies,but the foot ground rotary contact lacks effective evaluation and prediction measures.Therefore,it is very important to establish the contact mechanics model for the structured foot with soft terrain considering interaction forms under various attitude conditions.The interaction between the foot and ground for the plantigrade quadruped robot-Charlie developed by German Research Center for Artificial Intelligence synthesizes the contact forms of translation and rotation,so the quadruped mobile robot is more suitable to be the ideal platform in studying the robotic foot-terrain interaction.The experimental research on the translational and rotational contact of the robot's legs and feet with the ground is carried out in this paper,including the bionic contact experiment of the plantar foot with the ground.According to the contact between the translational leg and the ground,the experiments of translational quasi-static contact and normal dynamic impact are studied.Concerning on the rotary contact,the rotary experiments of flat plate and C-leg foot in sand were also carried out.Single peak value for supporting force and sine-like variation are found in terms of rotary contact between rectangular flat foot and terrain.Using the bionic contact experiment of human walking,the critical speed at which the plantigrade foot-terrain interaction force tranverses from double peaks to single one,as well as the relations among plantar parts during the whole foot-terrain contact cycle are obtained,which provides data support for the evaluation of the model prediction results and the form improvement.Based on spiral sliding theory,the interaction model between flat foot and sand is established.Based on ultimate bearing capacity theory,the mechanical model of horizontal strip structure contacting with sand and soil is established.The changing characteristics of Rankine active zone when the flat foot with conventional configurations contacts with sand are derived.For smooth,non smooth and compound geometry with flat feet,the integral models of passive pressures in three dimensions are established respectively.Based on the integral model and the simplified zero resultant moment equation,the normal/tangential contact mechanical models of circular and rectangular flat bottoms with sand are established respectively.By adding equation describing gradient characteristic for Rankine active zone,the error of the prediction model is reduced,and the validity of the model is verified by comparing predictions with the experimental results.The interaction model of curved foot and sand is established by using the spiral sliding condition modified by scale coefficient and exponential power.Based on Hansen model,the influence of tilt angle and width in three dimensions on the prediction results of foot-terrain interaction is studied.For the influence of the tilt attitude angle,the coefficient of ratio to the rotation angle is introduced;for the influence of the width,the equivalent width dominated by the rotation angle and ratio of the length to width is introduced.Finally,the improved foot ground contact mechanical model dominated by the ratio and equivalent width is established.This model is used to describe the contact stress between the inclined or horizontal bar element and sand.The contact forces between the various curved feet and the sand are obtained by integrating the stress on the action area of the cylindrical foot,spherical foot and C-shaped foot.Based on the established foot-terrain interaction model,the optimal design of the metatarsopod and C-shaped foot structure is guidingly carried out.According to the contact mechanics of heel to ground,forefoot to ground and total plantar area to ground,the evaluation index of walking performance is proposed.The index is taken as the optimization target to complete the design of foot size and physical parameters of connecting components.Based on the value,the influence of size and physical parameters on walking performance is analyzed.Based on the similar index,the radius and width of forearm C-shaped foot are designed.Finally,depending on the design schematic of one determined plantigrade quadruped robot,the kinematics and dynamics models of the robot are systematically established.Taking the planning motion gait and foot trajectory as input,a motion simulation system for plantigrade quadruped robot walking on soft terrain is developed,associated with foot-terrain interaction mechanics.The principle of influence of foot structure to walking abilities is obtained through comparing the simulation results such as joint torques and moving speeds,which verifies the practicality and validity of the improved foot-terrain interaction model based on its improvement towards application.This paper systematically studies the foot ground contact mechanics of a plantigrade quadruped robot,which has theoretical and practical significance in the future control planning and simulation application.