Pendubot Simulation Performance Leaderboard

Controller Short Controller Description Swingup Success Swingup Time [s] Energy [J] Max. Torque [Nm] Integrated Torque [Nms] Torque Cost [N²m²] Torque Smoothness [Nm] Velocity Cost [m²/s²] Real AI Score Username Data
iLQR MPC stabilization Online optimization with iterative LQR. Stabilization of iLQR trajectory. Top stabilization with LQR. True 4.19 9.14 1.75 2.8 2.04 0.019 136.95 0.845 fwiebe data plot video
iLQR Riccati Gains Stabilization of iLQR trajectorry with Riccati gains. Top stabilizaion with LQR. True 4.2 9.06 1.66 2.64 1.97 0.008 137.2 0.847 fwiebe data plot video
Energy PFL Partial Feedback Linearization with energy shaping control. Stabilization with LQR. True 4.8 53.75 3.0 12.28 33.06 0.136 870.16 0.594 fwiebe data plot video
iLQR MPC Online optimization with iterative LQR. Without reference trajectory. True 0.65 9.98 6.0 2.39 10.56 0.026 44.16 0.861 fwiebe data plot video
TVLQR Stabilization of iLQR trajectory with time-varying LQR. True 4.2 9.06 2.82 2.57 2.0 0.031 137.31 0.827 fwiebe data plot video


The simulation leaderboard compares the performance of different control methods in simulation. The task for the controller is to swingup and balance the pendubot and keep the end-effector above the threshold line.

The model parameters of the pendubot are:

More information about the dynamic model of the double pendulum can be found here: Double Pendulum Dynamics. For a urdf file with this model see here: URDF.

The pendubot is simulated with a Runge-Kutta 4 integrator with a timestep of \(dt = 0.002 \, \text{s}\) for \(T = 10 \, \text{s}\). The initial pendubot configuration is \(x_0 = (0, 0, 0, 0)\) (hanging down) and the goal is the unstable fixpoint at the upright configuration \(x_g = (\pi, 0, 0, 0)\). The upright position is considered to be reached when the end-effector is above the threshold line at \(h=0.45 \, \text{m}\) (origin at the mounting point).


For the evaluation multiple criteria are evaluated and weighted to calculate an overall score (Real AI Score). The criteria are:

These criteria are used to calculate the overall Real AI Score with the formula

\[ \begin{equation} S = c_{success} \left( w_{time}\frac{c_{time}}{n_{time}} + w_{energy}\frac{c_{energy}}{n_{energy}} + w_{\tau, max}\frac{c_{\tau, max}}{n_{\tau, max}} + w_{\tau, integ}\frac{c_{\tau, integ}}{n_{\tau, integ}} + w_{\tau, cost}\frac{c_{\tau, cost}}{n_{\tau, cost}} + w_{\tau, smooth}\frac{c_{\tau, smooth}}{n_{\tau, smooth}} + w_{vel, cost}\frac{c_{vel, cost}}{n_{vel, cost}} \right) \end{equation} \]

The weights and normalizations are:

Criterion normalization \(n\) weight \(w\)
Swingup Time 10.0 0.2
Energy 100.0 0.1
Max Torque 6.0 0.1
Integrated Torque 60.0 0.1
Torque Cost 360 0.1
Torque Smoothness 12.0 0.2
Velocity Cost 1000.0 0.2


If you want to participate in this leaderboard with your own controller have a look at the leaderboard explanation in the double pendulum repository. The leaderboard is automatically periodically updated based on the controllers that have been contributed to that repository.