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Four-legged Walking

For walking on four legs stability is rarely a limiting factor, but with irregular shaped legs, varying friction coefficients, motor limitations, and difficulties with modeling ground contact, choosing suitable leg trajectories becomes a complex optimization problem.

Excellent results can be achieved with machine learning techniques, e.g. utilizing Evolutionary Algorithms. With those the Aibos learned omni-directional gaits with top speeds of 50cm/s. This was so far unchallenged in 2005 and 2006, neither by Sony itself nor by other research groups.



Biped Walking

Walking on two leg is difficult for robots even on flat terrain. Ordinary servo motors are by far not as strong, fast, and accurate as muscles. Furthermore, the human nervous system provides far more sensor input than the few distinct sensors employed in common robots. And once the ground is not flat and rigid any more, but contains unevenness, bumps, or even soft and yielding spots, walking robots easily stumble and fall.

The challenge lies in developing fast and stable walking which enables smooth direction changes and takes sensor information into account to compensate uneven walking ground or external disturbances caused for example by unforeseen collision or by being pushed.

To achieve those goals research is done on different approaches.


Static Trajectories

This intuitive approach to development of walking patterns was originally implemented for the humanoid robot "Kondo KHR1" (see middle figure below) and later also applied to the robot "Bender" (right figure), which was designed and developed at the IRF. This approach is not restricted to two-legged motion but can and was applied also to four-legged motion as explained above. The general idea is to specify trajectories (curves) for the limbs which are periodically executed. For a suitable set of parameters the resulting motion can lead to stable walking. Those parameters include the shape of the trajectories themselves, the walking speed, duration of a single step, distances between the feet, phase shifts between motions of different body parts, etc.

TrajectoryKinematicLeg KHR1 Bender

This relatively simple approach has several advantages (beside its simplicity) that explain its frequent utilization for example in RoboCup. Besides intuitive calibration and independence of any sensor calibration, there is the easy access for using machine learning algorithms to optimize the walk for high speed. This optimization of the parameters implicitly takes care of the robot body's mechanical issues and the specific ground which is used during the optimization.


Static Center-of-Mass Trajectories

A further approach utilizing static trajectories currently under evaluation does not specify the limb movement directly, but rather the movement of the robot's center of mass (CoM). As stability criteria for biped walking the Zero Moment Point (ZMP) is commonly used. Figuratively speaking, this is the point on the ground where all tipping moments of the robot become zero. If this point lies inside the support polygon, i.e. inside the convex hull of all contact points to the ground, then the robot's posture or movement is stable. Choosing the CoM trajectory appropriately results in a ZMP trajectory which always lies inside the area of the support foot. Since the course of the center of mass is only restricted by the desired ZMP, this can be achieved by many different possible motions including natural human walking, where the CoM for example is not restricted to one height only.


Dynamic Approach

The approaches so far complicate the application of sensor data to stabilize the walking, since the chosen parameters are adapted for very specific external conditions. A change in those conditions leads to results that are not easy to calculate. And in most cases those ramifications can not be countered by adjusting one or two of the chosen parameters alone. For the application of sensors for stable walking a new approach is needed: to move the robot's center of mass using a control loop so that the measured ZMP followes the desired ZMP which is chosen to always lie inside the planned foot positions.




The figure shows the input trajectory for the desired ZMP (Yzmp) and the resulting CoM trajectory.


Measuring the ZMP in our given robots is a difficult task in itself, since the various sensors bring different pros and cons. In this approach we choose the measurement using pressure sensors in the feet. The ZMP can thus be measured as the center of pressure of all sensors. Originally this approach was developed for the robot Bender and later ported for use on the Nao to use in the RoboCup SPL for controlled walking and kicking.



Dynamic Approach using a Preview-Controller

A different way to design a controller for the task of dynamically stable walking includes the utilization of a preview controller. The given trajectory for the desired ZMP can be used to derive an optimal CoM trajectory which results in the desired stable motion. Here the acceleration sensor is used to measure the ZMP, forwarded into an observer which estimates position, velocity and acceleration of the center of mass. This estimation is used in a feed-back loop for the preview controller to control the further CoM trajectory accordingly.

ZMP-Regler 2

By using a preview of the ZMP trajectory of about 0.8 seconds it is possible to achieve almost any desired ZMP as long as it is mechanically possible, which offers additional freedom for choosing foot positions on the ground. This results in a fully omni-directional Walking Engine, i.e. any combination of translational and rotational speeds are possible as long as there are viable step pattern resulting in those.

Stability tests have been done in a simulated environment for the robot models Bioloid and Nao. Real world experiments have been conducted on Bender and Nao. For the Nao the approach was also successfully employed during the RoboCup 2008 and 2009 and in lab experiments on uneven / unstable ground.