The ZeBRo (Dutch abbreviation: Zesbenige Robot, six-legged robot), is a walking robot designed by the TU Delft, with its foundations on the RHex. The current version of the ZeBRo project, the DeciZebro, is made for the research to swarming in robotics, and is about the size of an
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The ZeBRo (Dutch abbreviation: Zesbenige Robot, six-legged robot), is a walking robot designed by the TU Delft, with its foundations on the RHex. The current version of the ZeBRo project, the DeciZebro, is made for the research to swarming in robotics, and is about the size of an A4-paper.

To counter these shortcomings of CPG (a method to determine gait movement), Max-Plus algebra can be used for the timing of the legs of walking robots. This can be done by modeling a walking cycle as two discrete events. These events are the times of the lift-off and touchdown and can be determined by using a Max-Plus Discrete Event System (DES) framework. The main purpose of these events is to determine two separate periods; the stance period, and the swing or flight period.

Max-Plus algebra is defined as a semi-ring over the union of real numbers and minus infinity. The standard binary operations are taking the maximum and addition which can be used for scalar and matrix operations.

The Max-Plus linear system contain the gait matrix A, and the vector v(k) containing the lift-off and touchdown times of vector instance k. One of the strengths of this method is the ability to change gaits, by simply changing the A-matrix. This then results in the switching Max-Plus linear (SMPL) system:

This SPML system determined in only contains gaits with successive recirculating leg-groups, where the synchronization of the lift-off of a certain leg-group I relies on the touchdown of the leg-group i-1. This allows for gaits like walking for humans, or a slow trot for horses, where a leg-group remains on the ground until the previous leg-group has recirculated.

To increase the number of possible gaits, the synchronization of successive leg-groups is extended to not only contain the previous leg-groups' touchdown times, but also their lift-off times. This extension allows for gaits containing multiple rotation leg-groups at the same time, making gaits like the gallop possible. Because of the desired stable situation of grounded legs, the synchronization is chosen to not extend the timing of the touchdown, as delays should not hinder the return of the legs to their grounded position.

The performance of different gaits is tested on different surfaces, to determine the influence of the amount of legs on the ground and determining whether gait changes could influence the success rate of the system regarding traversing rough terrain. Inertia measurement units (IMU) are used for detecting rough terrain, and tests show that the body movement of a ZeBRo on both flat and rough terrain are heavily influenced by the gaits used.

Because of several limitations regarding the actuation of the legs, gaits containing moments of static instability could not be tested. However, the framework for implementation regarding the Max-Plus is lain and tested using simulations.