Cubli is a robot of a alone degree of freedom that can jump and balance in the corners.
Cubli General Terms
The reaction wheels mounted on three sides of the hub rotate at high angular speed and then brake suddenly, causing the Cubli to bounce upward. When the Cubli is almost stopped in a corner, controlled torque is applied to keep it balanced in the corner. In addition to balance, torque can be used for controlled descent, allowing the Cubli to be ordered to fall in any direction. By combining these three skills (jumping, balance, and controlled falling), Cubli can “walk”. The power, computer, and control components were not assembled into the prototype to prevent the first prototype from being too complex.
Design from Cubli
The inverted pendulum system has a very rich history and has been widely used to test, demonstrate and compare new management concepts and theories. Furthermore, the development of new control algorithms for the pendulum system itself remains an active area of research. Compared to other 3D inverted pendulum test benches, Cubli has two unique features. One is its relatively small footprint (hence the name Cubli, derived from the Swiss German abbreviation for “cube”).
Another feature is its ability to jump from a stationary position without external support, an interesting concept not only for control engineers, but also an attractive demonstration for the public.
image. Figure 2 shows Cubli's jump strategy. An initially asleep Cubli will jump to the side and immediately stop one of the auxiliary wheels. Once completed, Cubli will provide a low-cost open source testing platform with a relatively small footprint for the evaluation and control of research and education.
Due to the rigidity of the structure and the limitations of the ready-to-use components, only the drive wheel has sufficient design flexibility for Cubli's mass distribution characteristics. Assuming that the collision between the drive wheel and the pendulum is perfectly inelastic, calculate the angular velocity of the drive wheel required for the rebound.
Although it is possible to reduce the high angular velocity of the wheel before braking by increasing the inertia of the wheel, i.e. increasing the mass of the wheel due to the limited size of the wheel, it is not taken to the ends, as it leads to a decrease in the recovery angle during balancing.
A gear chain between the wheels and the motor is eliminated, as it prevents high angular velocity jumps and increased weight and volume. Although balancing operations requiring high torque would be compromised by the gearless choice, BLDC motors can still provide enough torque for recovery angles of up to 7°.
Figure 3 shows the 1D prototype built to test the feasibility of Cubli and design the control algorithm. Inverted pendulums based on interchange drive wheels are constructed similarly except for the braking mechanism.
The prototype consists of a square plastic plate that holds a drive wheel with a motor in the middle and a brake mechanism in one of the corners. The dimensions of the plastic sheet coincide with the dimensions of the proposed Cubli surface, hereinafter referred to as the pendulum. The plate is connected to bearings at the bottom, giving it a degree of freedom to rotate at a corner in a horizontal plane.
Electronic componentss
The power, computing, and control components were not assembled in the 1D prototype so that the first prototype would not be too complex. Figure 5 shows the general configuration of the electronics, except for the power provided by the constant voltage power supply.
We chose the STMicroelectronics STM3210E evaluation board (equipped with a Cortex-M3 synchronized to 72 MHz) as the primary controller for rapid prototyping and out-of-the-box community support. The IMU consists of a 3-axis accelerometer, Analog Devices ADXL345, and a 3-axis gyroscope using the InvenSense IDG-500/ISZ-500 series. As shown in Figure 6, two IMUs are mounted on the pendulum and connected to the evaluation board via two independent serial peripheral interface (SPI) buses.
A Maxon Motor AG EC-45 50W brushless flat DC motor was chosen for the drive wheels due to its higher energy density compared to brush-driven DC motors. The motor is controlled by a standard Maxon EPOS2 50/5 four-quadrant digital motor controller. The CANopen protocol is used for communication between the engine control and the evaluation board.
Please note that all Cubli will use a miniature version of the previous controller, the DEC 36/2 module. The HSG-5084MG servo RC brake mechanism is driven by the PPM signal from the evaluation plate. For debugging purposes, a high-speed rotary magnetic encoder RE36 is used to measure θb, which is connected to a timer/counter unit on the evaluation board.
The framework uses the FreeRTOS scheduler's STM32 port due to the priority multitasking capabilities provided by the scheduler and the small binary kernel (4kB) image. ODeV, a completely free and open source embedded systems development environment based on Eclipse IDE, was used for software development. * Specifications vary for each version as different researchers develop different versions. You can find information about each unique specification using the references below.
Cubli specifications
| Height | 15 | cm |
| Width | 15 | cm |
| Length | 15 | cm |
| Controller | STM32 discovery board (ARM7 Cortex-M4, 168 MHz) | |
| IMU (inertial unit of measurement) | 6 | (MPU6050, InvenSense |
| (consists of a speed gyroscope and an accelerometer) | ||
| DC motor | 3 | brushless EC-45- flat (Maxon Motor AG) |
References of interest
Development of a Nonlinear Mechatronic Cube
The thesis focuses on both the theoretical and physical development of the cube. The different control methods for the balance cube are developed and validated using theoretical simulation models and tested on the constructed cube.
E. Bjrke, B. Pehrsson. – Master of Science Thesis, 2016.
A review of Cubli and the nonlinear control strategy
The work related to Cubli, its design, and the methodology behind Cubli's operation are reviewed. Work related to nonlinear optimization is presented to discover the best possible way to balance the Cubli in its corners.
R. Singh, V. Tayal, H. Singh, et al. – Conference: IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems, 2016.
The Cubli: a 3D inverted pendulum based on a reaction wheel
The mechatronic design is presented. The dynamics of the multibody system are derived and the parameters of the nonlinear system are identified. The corner balancing controller is presented along with the experimental results.
M. Gajamohan, M. Muehlebach, T. Widmer, et al. – European Control Conference (ECC), July 2013.
Nonlinear analysis and control of a 3D inverted pendulum based on a reaction wheel
Describe the control and learning algorithms used. Dynamics followed by control are introduced. Aspects related to jumping are covered and experimental results are presented.
M. Muehlebach, R. D'Andrea. – 52nd IEEE Conference on Decision and Control, December 2013.
The Cubli: a cube that can jump and balance
It presents the concept of Cubli along with the development of one-dimensional design, modeling, identification and control. Describe a control procedure to eliminate sensor offsets during the balancing maneuver.
M. Gajamohan, M. Merz, I. Thommen, et al. – IEEE/RSJ International Conference on Robots and Intelligent Systems, October 2012.