Ankle torques have four states. Various state transfers were performed using the conditions of whether the foot touched the ground, the height of the ankle joint, the ankle angle and the hip angle. B Overall controller of bipedal robot. To test the effect of the ankle push-off torque and push-off height the push-off height is the height of the ankle joint of the swing leg on the robot's walking speed, the ankle torque state machine was designed to perform different ankle torques on the robot.
Taking the left leg ankle torque state machine as an example, the states of the transfer processes of the ankle torque are explained in detail. Then, the ankle push-off of the left leg is triggered, and the ankle joint is actuated in the active mode. To prevent the foot from scuffing the ground during the swing period, the ankle torque state machine limits the ankle angle to the appropriate range. In the study, ankle push-off occurred before the heel strike, and the knee flexion of the trailing leg was determined by whether or not the leading leg touched the ground.
Thus, the knee joint is in extension when ankle push-off of the trailing leg occurs. To prevent the phenomenon that impulsive ankle push-off leads to the catapult-like action of the robot during the knee is in extension Lipfert et al.
The correction method of the ankle push-off torque is to plan a smooth fifth-order polynomial curve within 0. The curve is smooth from the beginning to the end. Both the step length and the walking speed are affected by ankle push-off Dean and Kuo, , and the walking speed increases with the step length.
This study aims to explore the effect of the torque magnitude of ankle push-off on the walking speed, so the step length is set to a fixed value. The initial position of the biped robot is that the left leg is the leading leg and the right leg is the trailing leg.
The left leg foot heel and the right leg foot toe touch the ground. In the planning trajectory, it takes 0. To make the robot walk normally, we apply a thrust to the robot's torso at the initial state.
The purpose is to make the robot's COM position exceed the highest point of the inverted pendulum so that it does not fall backward. The GRF, the actual trajectory of the joint and the joint torque are obtained. The average COM speed in the horizontal direction is used as the walking speed of the biped robot. The simulation model biped robot has components. The mass mi of each component is defined according to the material properties of the component.
Every component's COM position xi, yi, zi relative to the global coordinate system is recorded by using the transform sensor in the Simscape toolbox. The total mass of the robot M is The simulated model can acquire the continuous walking for at least 30s.
This study imitates the effects of the impulsive ankle push-off in human walking and explores the influence of the ankle push-off torque and push-off height on the walking speed for the planar biped robot. The robot mass in this simulation is The push-off height is measured from the ankle joint of the swing leg to the ground.
When the foot completely touches the ground, the height of the ankle is approximately 6. The range of the push-off height is set as 11—16 cm. The push-off height is roughly proportional to the gait cycle. Taking the average speed of the robot's COM as an index, the relationship between the push-off torque, the push-off height and the walking speed is tested.
The average speed of the COM, joint angle, and joint torque of the robot are mainly analyzed. The GRF is used to determine whether the foot touches the ground. One gait cycle is defined from the leg touch-down to the subsequent touch-down of the same leg, including the stance phase and the swing phase.
The normalized speed is calculated by the ratio of instantaneous speed to the maximum speed. In addition, to compare the ankle joint torque between humans and the simulation model at normal walking speeds, the ankle joint torque of the simulation robot is normalized to the body mass. We studied the effects of the ankle push-off torque on the walking speed of the biped robot.
When the push-off torque is in the range of When the push-off torque is Landscape of the walking speed of the biped robot with various sets of the push-off torque and push-off height. To explore the reason that the robot's walking speed increases during the process of the push-off torque increasing from 17 to Thus, the ankle push-off accelerates the movement of the swing leg and increases the walking speed of the robot, which is consistent with the conclusion proposed by Lipfert et al.
As the ankle push-off torque increases to With an increasing ankle push-off torque, the fluctuation of the instantaneous speed is reduced, and the walking speed of the biped robot is increased.
The normalized speed also shows a fluctuation from 0. In summary, the ankle push-off helps to increase the COM speed of the robot during the walking gait. Ankle push-off torque and normalized walking speed during the gait cycle. D Push torque is The light gray areas indicate the stance phase, and the non-shaded areas indicate the swing phase. Furthermore, the joint kinematics are obtained at different ankle push-off torques 17, 18, 19, and It can be seen from Figures 5A,B that the movement patterns of the hip and knee joints are basically similar.
Under the condition of different ankle push-off torques, the timing difference of the knee starting to flex is small, but the timing difference of the knee joint finishing the flexion and extension is large, as shown in Figure 5B. When the push-off torque increases to This result also shows that the movement of the knee joint is consistent with the movement of the hip joint, as shown in Figures 5A,B. The motion curve of the ankle joint is shown in Figure 5C.
With the foot entirely in contact with the ground, the body moves forward with the shank rotating around the ankle joint. The ankle begins to flex, and the joint angle gradually decreases. Until the ankle push-off conditions are satisfied, the ankle torque begins to change from a passive underactuated mode to an active actuated mode. At this time, the push-off torque is applied to the ankle, so the ankle starts to extend and the ankle angle starts to increase, as shown in Figure 5C. When the swing leg moves to the front of the body, i.
The ankle joint push-off torque is switched from the active actuated mode back to the passive underactuated mode in preparation for the next touch-down. Robot joint kinematics during one gait cycle: A Hip angle. B Knee angle. C Ankle angle. The red, blue and pink solid lines correspond to the joint kinematics when the ankle joint push-off torques are 18, 19, and To study whether the ankle push-off of the robot had a positive effect on walking speed, similar to the role of ankle push-off during human walking, the joint kinematics and ankle torques of the simulated robot at 1.
The human data are taken from the literature Geng and Gan, ; Lipfert, The size parameters of bipedal robot are similar to the adult humans.
Figure 6 presents the joint angle comparison between the simulation robot and human at a normal walking speed. The results show that the hip and knee joints of the simulation robot and human have similar motion patterns at a normal walking speed. The range of motion of the hip joint of the simulation robot is larger than that of humans Figure 6A , but the range of motion of the knee joint is smaller than that of humans Figure 6B.
Notably, the motion pattern of the ankle joint of the simulation robot is similar to that of a human. Two peak waves of the ankle angle are observed during walking of the simulation robot, i. Joint kinematics of the simulation robot and a human at a normal walking speed.
A—C show the motion curves of the hip, knee, and ankle joints, respectively. The black solid line indicates the joint kinematics of the simulation robot, and the red dashed line indicates the joint kinematics of the human during normal walking speed.
Y lateral and Z vertical translations of the torso center of mass. The translation in the Z direction is normalized to a similar range as the other observations.
The robot torso center of mass is less than 0. The following reward function r t , which is provided at every time step is inspired by [2]. Ts is the sample time of the environment. This reward function encourages the agent to move forward by providing a positive reward for positive forward velocity. It also encourages the agent to avoid episode termination by providing a constant reward 25 Ts Tf at every time step.
The other terms in the reward function are penalties for substantial changes in lateral and vertical translations, and for the use of excess control effort. To simulate the robot with the agent of your choice, set the AgentSelection flag accordingly. A DDPG agent approximates the long-term reward given observations and actions using a critic value function representation.
A DDPG agent decides which action to take given observations by using an actor representation. The actor and critic networks for this example are inspired by [1]. For more information on creating a deep neural network value function representation, see Create Policy and Value Function Representations. A TD3 agent approximates the long-term reward given observations and actions using two critic value function representations.
A TD3 agent decides which action to take given observations using an actor representation. The structure of the actor and critic networks used for this agent are the same as the ones used for DDPG agent. Since the agent uses the Q value to update its policy actor , the resultant policy can be suboptimal and accumulating training errors can lead to divergent behavior. Two critic networks — TD3 agents learn two critic networks independently and use the minimum value function estimate to update the actor policy.
Doing so prevents accumulation of error in subsequent steps and overestimation of Q values. Addition of target policy noise — Adding clipped noise to value functions smooths out Q function values over similar actions. Doing so prevents learning an incorrect sharp peak of noisy value estimate. Delayed policy and target updates — For a TD3 agent, delaying the actor network update allows more time for the Q function to reduce error get closer to the required target before updating the policy.
To leave a comment, please click here to sign in to your MathWorks Account or create a new one. Toggle Main Navigation. Search MathWorks. Guy on Simulink. Deep Learning. Developer Zone. Behind the Headlines. File Exchange Pick of the Week. Hans on IoT. Student Lounge. Toggle navigation. Motivation First of all… why simulate? Safety: Robots will fall. Prototypes will break. You can verify that controls algorithms are at a good starting point in simulation before moving to hardware.
Simulation lets you test your robot and controller design under multiple scenarios without building prototypes. In simulation, you also get the benefit of intentionally generating unsafe conditions, as well as discovering unexpected issues. Efficiency: Physical experiments take time and effort to set up and reset between runs. With simulation, you get a programmatic environment to automate experiments and walk away from your desk.
Related Information. Watch other Modeling Simulation and Control videos 19 videos. Featured Product Simscape Multibody. Optimizing Walking Robot Trajectories. Related Videos:. Multibody Simulation with Simscape Multibody. Physical Modeling: Building a Rotary Pendulum.
0コメント