The High-level Commander has been part of the Crazyflie firmware since the 2018.10 release. In combination with a positioning system, it can fly the Crazyflie along a trajectory that is either defined in the firmware or uploaded through the python lib. It originates from the Crazyswarm project and we have used it in various demos since it is possible to make trajectories that are very fluid and looks really cool. The trajectories are defined as 7th degree polynomials describing segments executed one after each other.

The controller gives full control of position, velocity, acceleration and jerk, the only problem is that it is non-trivial to generate the polynomials. We have wanted to simplify the creation of trajectories for a long time and have finally had some time to play with it. In this blog post we will describe how it can be done with Bezier curves and show some examples.

Each segment in a High-level commander trajectory is defined by four 7 degree polynomials, one for x, y, z and yaw. There is also a scaling parameter that tells the controller the time scale to use when executing the segment. Using polynomials of degree 7 makes it possible to design trajectories that are continuous in position, velocity, acceleration and jerk when changing from one segment to the next, which is important to get a smooth and controlled flight.

Bezier curves are common in many graphics applications and are probably known to most users. They are parametric curves defined by control points, usually three or four. Bezier curves can also be expressed as a polynomial, and this is what we will use in this case. To get a correct mapping to the desired polynomials we need some more control points and will use 8 per segment. The basic idea is to define the trajectory as Bezier curves and make sure the control points are placed in such a way that the continuity requirements are satisfied.

On this page from University of Cambridge, there is a good explanation on continuity across the joins between curves and formulas for c0, c1 and c2 continuity. We also need c3 continuity which can be calculated in the same manner

With these formulas it is possible to set the handles of the Bezier curves to make sure we get a smooth ride.

We have added a python example that implements the ideas above. You can find it in crazyflie-lib-python/examples/positioning/bezier_trajectory.py. The design is based on Nodes that represents the connection points between bezier curves (called Segments). The Nodes has a set of handles that are shared between the Segments that use the Node. If not all handles are set the implementation will set them to appropriate values, see the comments in the code for more details. The Node API only allows the user to set handles on one of the Segments, the handles for the other segment are automatically set to generate a continuous trajectory.

The example uses nodes in the corners of a square and contains three parts:

Velocity in the nodes. A fluid motion all the way around.

Finally a video showing the full sequence, we use the Lighthouse for positioning.

3 of us where at ICRA 2019 in Montreal last week, where we met a lot of interesting people and a lot of Crazyflie users. Thanks a lot to everyone that drop by our booth, and for the ones that missed it we are planning on being at iROS2019 later this year so we might see you there :-).

We have already described our demo in a previous post, now that we run it we can update on how it went. We are also updating the ICRA2019 page with the latest source code and information so that anyone interested can reproduce the demo.

In its final state at the conference, the demo contained 8 Crazyflies 2.1 equiped with Lighthouse deck and Qi charger deck. There were 8 3D-printed charging pads on the floor with Ikea Qi wireless chargers and two HTC Vive base stations (V1) on tripods. The full system was contained in a cage, built from 50 cm-long tubes or aluminium and nets.

The full setup of the booth took us about 4 hours, this included about 3 hours for the cage, 15 min for the demo including calibration of the lighthouse base-station geometry and the rest to fine-tune things. This is by far our best setup time, we still need to prettify the cage a bit and to make is easier to install, but we will most likely re-use this system for upcoming conferences.

In this demo we aimed at keeping a Crazyflie in the air at every moment, to do so we had a computer connected to all 8 Crazyflies sending to one of them the signal to start flying if no other where actually in the air flying a trajectory. The flight was completly autonomous as we explained in our previous blog post. We setup the Crazyflie to fly 2 cycles and then land, which increase the rate of swap and so increased the ‘action’, though it also meant that during the swap two Crazyflies where flying. This drained the batteries a bit more than expected and meant that after about an hour all the Crazyflies where bellow the take-off threshold and we had to wait ~30 seconds between flights. Here is a video of it in action:

The demo was very care-free, we had very few Crashes and we mostly restarted the Crazyflies to swap batteries manually to add a bit of power in the swarm. The last day we decided to spice it up a little bit by adding a chair in the cage and by calibrating the chair position and flight trajectory, we managed to have the Crazyflie partly fly under it. This worked quite well most of the time and showed that the lighthouse positioning is repeatable and works fairly well with short occlusion in the path. Though we also found out that even though a single Crazyflie would always fly the same trajectory, two different Crazyflies will not. We think differences in propeller stiffness and the fact that the our Mellinger position controller has not been calibrated for changing YAW are the main reasons.

If you want to know more about the demo or if you want to reproduce it do not hesitate to visit the ICRA 2019 page that explains it in more details and links to the source code of everything including 3D printed parts for the cage and the landing pads.