The under-actuated foot rotation that the heel of the stance leg lifts off the ground and the body rotates around the stance toe is an important feature in human walking. However, it is absent in the realized walking gait for the majority of biped robots because of the difficulty and complexity in the control it brings about. In this paper, a hybrid control approach aiming to integrate the main characteristics of human walking into a simulated seven-link biped robot is presented and then verified with simulations.
The bipedal robotic gait includes a fully actuated single support phase with the stance heel supporting the body, an under-actuated single support phase, with the stance toe supporting the body, and an instantaneous double support phase when the two legs exchange their roles. The walking controller combines virtual force control and foot placement control, which are applied to the stance leg and the swing leg, respectively.
The virtual force control assumes that there is a virtual force which can generate the desired torso motion on the center of mass of the torso link, and then the virtual force is applied through the real torques on each actuated joint of the stance leg to create the same effect that the virtual force would have created. The foot placement control uses a path tracking controller to follow the predefined trajectory of the swing foot when walking forward. The trajectories of the torso and the swing foot are generated based on the cart-cable model. Co-simulations in Adams and MATLAB show that the desired gait is achieved with a biped robot under the action of the proposed method.
In order to reproduce anthropomorphic walking on a biped robot, it is important to study and understand the walking pattern of humans. Human walking is the repetition of a basic movement, namely, the step. Generally, a normal step can be roughly divided into two successive phases according to the foot contact with the ground: the double support phase (or the stance phase), when both feet are on the ground, and the single support phase (or the swing phase), when only one foot is in contact with the ground. Figure 1 shows a single gait cycle, from when one foot strikes the ground with its heel to when the other foot strikes the ground.
Considering that the high dimensional walking task can be viewed as a collection of several decoupled task of lower dimensionality, the control of the biped robot is decoupled into two tasks, i.e., the control of the torso to track the desired motion, and the control of the swing leg to follow the predefined foot placement point. Therefore, a hybrid control scheme is proposed in this paper. The control scheme combines the ideas of virtual force control and foot placement control, which are applied on the stance leg and the swing leg, respectively. The working principle of the hybrid control scheme as illustrated in Figure 4 is detailed below.
The role of the walking pattern generator is to output the desired trajectories of the CoM of the torso and the swing foot. In this paper, the cart-cable model shown in Figure 5 is adopted, with the cart representing the CoM of the robot, and the foot of the table representing the stance foot of the robot. It is assumed that the mass of the biped robot is lumped with the CoM of the robot, and the CoM is kept at a constant height. Based on the model, the relationship between the trajectories of the CoM and the reference ZMP can be described.
The main physical parameters of the biped robot model are shown in Table 1. The lengths of the links from the torso to the foot are 0.4, 0.37, 0.36 and 0.21 m, respectively. Their corresponding masses are 3, 1.8, 1.5 and 0.3 kg respectively. The planned duration of the heel support phase is 0.4 s, and the toe support phase is 0.3 s. In the implementation of the hybrid control scheme, the main work is to tune the parameters of the controllers by trial and error. If the parameters are selected appropriately, the desired walking pattern can be realized. Figure 7 shows the screenshots of the realized bipedal robotic walking in one cycle.
CONCLUSIONS AND DISCUSSION
This paper introduces a solution to the problem of the realization of human-like bipedal robotic walking with under-actuated foot rotation. The studied biped robot model is a planar seven-like biped robot with feet. The desired gait includes three successive phases, i.e., a fully actuated phase where the heel supports the body, an under-actuated phase where the toe supports the body, and an instantaneous double support phase where the foot–ground impact takes place and the two legs exchange their roles. To achieve this gait, a hybrid walking controller is proposed by combining virtual force control and foot placement control, which are applied on the stance leg and the swing leg, respectively.
The controller decouples the high-dimensional dynamic walking into two simpler tasks of lower dimensionality. Therefore, compared with the current methods, fewer control efforts and computation are required to realize human-like walking on a biped robot. The validity of the proposed approach is verified by co-simulations in Adams and MATLAB. However, there are still limitations in this paper. The double support phase, different from the human walking pattern, is assumed to be instantaneous. In the future, we will add the finite-time double support phase to the bipedal robotic walking gait. We will also study the implementation of the hybrid control approach on a physical biped robot prototype.
Source: Northwestern University
Authors: Yixiang Liu | Xizhe Zang | Shuai Heng | Zhenkun Lin | Jie Zhao