Research On Motion Planning For Legged Robots Based On Trajectory Optimization

Legged robots behave powerful locomotion abilities and are able to adjust to rough terrain.There are many applications in the military and disaster scenes.A lot of researches have been done in the recent decade.Many control methods,however,used hand-crafted motion.For complex tasks,it is difficult to hand-craft motions which are physically correct.In order to extend the application scenes of legged robots,a kind of method of motion planning for legged robots which can translates a high-level task into a desired motion-plan for a legged robot to execute is necessary.The difficulty of legged robot motion planning is that the position and pose of the robot cannot be controlled directly,and it must be adjusted by the contact force generated by the contact between the end effector(foot or hand)and the environment.In addition,these contact forces acting on the end effector must comply with many constraints.For example,only when the foot end contacts the ground can the force be generated,which further increases the difficulty of the control and motion planning of legged robot.When there are many possible contact points between the robot and the environment,the possible contact schedule between the robot and the environment will grows exponentially.For example,the quadruped robot can land on one leg or on diagonal legs,and the hexapod robot can have more ways to contact the ground.When there are many possible contact points,it is difficult to specify the contact order of each point for complex tasks.At the same time,specifying the contact schedule of each contact point will greatly limit the possible motion of the robot.Furthermore,physically valid motion cannot be generated with a specific contact order.When different robot feet touch the ground,the action points of force are different,and the dynamic model of robot is also different.For the legged robot with many contact points,it is difficult to establish the dynamic model for each contact mode one by one.How to consider the various constraints of contact force into the motion planning of the legged robot;how to establish a unified dynamic model of the legged robot without having to model the contact environment of each robot one by one;how to automatically explore various contact modes without having to specify in advance.This thesis will focus on these issues.In this thesis,complementary constraints are used to model the contact,and a unified dynamic model is established.It is not necessary to model each contact mode of the legged robot separately.Complementary constraints also take into account various constraints of contact force.It is a reasonable model for legged robot.Based on trajectory optimization,the motion planning problem of the legged robot is transformed into a trajectory optimization problem.The direct method of trajectory optimization is used to further transform the motion planning problem of the legged robot into a nonlinear optimization problem,which can be solved by a generic nonlinear optimization solver.The robot state,control,ground reaction force,contact schedule of end effector,swing-leg trajectory and footholds are determined by solving nonlinear optimization problems.A planar biped robot is used to generate stable periodic walking motion by using the motion planning method introduced in this thesis,and the feasibility of the motion planning algorithm is preliminarily illustrated.In order to verify the performance of the motion generated by the motion planning algorithm on the real robot,this thesis makes a more in-depth study on a hexapod robot,and uses the motion planning algorithm to generate the motion of the hexapod robot such as straightline walking,turning and spinning.The generated motions have been tested on the simulation environment and the prototype of the hexapod robot.The behavior of the generated motions is similar both in the simulation and on the prototype,which shows that the motion planning algorithm in this thesis can give a reasonable motion.This motion planning algorithm of legged robot can construct unified dynamics model,include all restrictions of contact force and automatically explore the contact mode,which can generate physically correct motion.