Advanced Biped Locomotion in Real/Simulated Humanoid Robots
Abstract
The goal of this project is to study the control of biped locomotion for a humanoid robot. A CPG-based controller was design so that the robot can walk at different speeds. The controller will have to be robust against perturbations, it means it should not fall if
4. Optimizing a Reference Controller
5. Improving the Reference Controller
6. In Need for a Toe
Summary
The goal of this project was to study the control of biped locomotion for a humanoid robot (Fujitsu HOAP-2). A CPG-based controller was designed so that the robot can walk at different speeds. The controller robustness was tested against perturbations as the robot should not fall if someone pushes it a little. To produce a more human-like gait, a toe was added to the feet of the robot. The toe was realized in two variants: with linear and non-linear stiffness and damping profiles.
Sine-based trajectories already have demonstrated their capability to be used for biped locomotion. However, they are not really adapted to a precise robot mechanical structure. More adapted trajectories were generated by a monotonic cubic interpolation (e.g. figures 1 and 2). The points to interpolate were generated by the optimization algorithm i.e. particle swarm optimization.
A new fitness evaluation procedure was used in order to integrate robustness features in the optimization process. The experiments were realized for three different walking velocities: 0.14 m/s, 0.28 m/s, 0.42 m/s using a Webots model of the robot. It was then possible to obtain gaits which were capable of heel-to-toe transitions and which looked human-like. The trajectories of the joints of one such kind of gait can be seen in figure 1.
The HOAP-2 robot’s feet degrees of freedom are present only in the ankle. There is no articulation at the top of the feet. This can lead to controllers which present two undesirable properties. Either the foot is maintained as parallel to the ground as possible which then results in a slow and clumsy gait, or the robot presents a heel-to-toe transition and all the weight of the robot is applied on a very small part of the foot. This behavior can lead to instabilities in the gait such as spinning. Thus, the Webots model of the robot was modified to integrate an additional toe on each foot.
Figure 1: Trajectories optimized by the controller to drive the robot joints. The robot target speed was 0.28 m/s. The gait produced looks natural and human-like.
Figure 2: Trajectories optimized by the controller to drive the robot joints. The robot target speed was 0.42 m/s. The robot model contained the additional toes with linear stiffness and damping profiles. The resulting gait presents a heel-to-toe transition.
The goal was to increase the duration of the foot-ground contact, and also to offer the possibility of energy storage. Two variants were realized: linear and non-linear stiffness and damping profiles. The experiments did not indicate the presence of energy storage. In fact the solution which presented the most human-like gait used a spring constant close to 0. The trajectories of the joints of this particular solution can be seen in figure 2. Finally the better controllers of each experiment were evaluated for robustness by applying localized perturbations.
The results indicate that the slower controllers are more unstable. The utilization of stiffness and damping profiles did not turned worthwhile as those controllers were outperformed by the other ones. The controllers optimized for 0.42 m/s target speed (with and without toes) turned out to be the most resilient to the external perturbations. Both were optimized targeting the faster robot speed. The former was optimized for the regular robot model whereas the later used a toe with a linear stiffness and damping profiles. The addition of the toe increased the force amplitude the robot could withstand in most cases.