Planning and Control of Humanoid Robots

Vision-Based Trajectory Control for Humanoid Navigation

Snapshots of experiments - line trajectory.          Snapshots of experiments - sigmoid trajectory.

Consider the problem of robustly tracking a desired workspace trajectory with a humanoid robot. In [1], we propose a solution based on the definition of a suitable controlled output, which represents an averaged motion of the torso after cancellation of the sway oscillation. The torso motion is reconstructed using the vision-based odometric localization method previously presented in [2] and described here. For control design purposes, a unicycle-like model is associated to the evolution of the output signal. The following block scheme summarizes the developed control paradigm.

control block scheme

Sway motion cancellation

Two different techniques have been used to achieve cancellation of the sway motion, i.e. the natural transversal oscillation of the torso during locomotion. The first proceeds from the observation that swaying is a relatively high-frequency phenomenon, and therefore it may be removed by a suitable low-pass filter (with cut-off frequency of 0.8 Hz). The second technique uses a geometric projection based on kinematic computation to cancel the lateral movement of the torso during locomotion. The plots below show the results of the two techniques on the same torso motion (Left: low-pass filtering; Right: geometric projection). Both are effective in isolating an averaged torso motion.

Sway motion cancellation - low-pass filtering output.          Sway motion cancellation - geometric projection output.
Experiments

To validate the proposed trajectory control scheme, we performed some experiments on the humanoid robot NAO (version 4.0) by Aldebaran Robotics. In our implementation, the controller updates the robot driving and steering velocity inputs at 100 Hz. These commands are then sent to the robot using the NAO APIs, and in particular the built-in move function. Since the most recent command overrides all previous commands, this function can be called with arbitrary rate, thus providing a convenient mechanism for real-time implementation of a high-level control loop.

Desired trajectory: line

In the first tracking experiment, the desired trajectory is a line.

These are the results obtained using low-pass filtering for sway motion cancellation.

Experimental results, low-pass filtering, trajectory: line.          Experimental results, filtered vs desired, trajectory: line.

In particular, the left plot shows the desired trajectory vs. the actual trajectory of the torso, as estimated by our odometric localization algorithm, whereas the right plot shows the controlled variable vs. the reference signal. The root mean square of the cartesian error is 0.0330 m in this case.

For comparison, here are the corresponding results obtained using geometric projection for sway motion cancellation. The rms error in this case is slightly larger (0.0808 m).

Experimental results, geometric projection, trajectory: line.          Experimental results, projected vs desired, trajectory: line.

Desired trajectory: sigmoid

In the second experiment, the desired trajectory is sigmoidal.

As shown below, results are satisfactory for both sway cancellation methods, again with a slight advantage for low-pass filtering (first row, rms error is 0.0186 m) that achieves a slightly smoother motion w.r.t. geometric projection (second row, rms error is 0.0191 m).

Experimental results, low-pass filtering, trajectory: sigmoid.          Experimental results, filtered vs desired, trajectory: sigmoid.

Experimental results, geometric projection, trajectory: sigmoid.          Experimental results, projected vs desired, trajectory: sigmoid.

Video clip

The following clip illustrates the experiments.

Documents

[1] G. Oriolo, A. Paolillo, L. Rosa and M. Vendittelli, Vision-Based Trajectory Control for Humanoid Navigation. 2013 IEEE-RAS Int. Conf. on Humanoid Robots, Atlanta, GA, Oct 2013 (pdf). 

[2] G. Oriolo, A. Paolillo, L. Rosa and M. Vendittelli, Vision-Based Odometric Localization for Humanoids using a Kinematic EKF. 2012 IEEE-RAS Int. Conf. on Humanoid Robots, Osaka, Japan, Nov-Dec 2012 (pdf).

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