Covariance of the contact position noise $\Sigma_p = \begin{bmatrix} 0.4^2,&0.4^2,& 0.4^2 \newline
0.4^2,& 0.4^2,& 0.4^2\newline
0.4^2,& 0.4^2,& 0.4^2\end{bmatrix}$
SCP forces:
DDP tracking SCP forces:
Pybullet monte-carlo simulations:
I ran 100 monte-carlo simulations while adding a sampled random forces from the covariance of the linear momentum at the center of the robot base, then checked if the contact forces from pybullet is inside the friction cone constraints.
no. of constraint violations from DDP tracking nominal SCP = 20183
no. of constraint violations from DDP tracking stochastic SCP = 14630
avg. cost nominal = 1.807048631332169
avg. cost stochastic = 2.022525420858646
Trot motion
dt = 0.01 Gait parameters = {'stepLength' : 0.1, 'stepHeight' : 0.05, 'stepKnots' : 25, 'supportKnots' : 10, 'nbSteps': 3} Covariance of additive white noise on centroidal dynamics $\Sigma_w = \begin{bmatrix} 0.6^2,& 0.5^2,& 0.3^2 \newline 0.7^2,& 0.5^2,& 0.3^2\newline 0.5^2,& 0.4^2,& 0.3^2\end{bmatrix}$
Covariance of the contact position noise $\Sigma_p = \begin{bmatrix} 0.4^2,&0.4^2,& 0.4^2 \newline 0.4^2,& 0.4^2,& 0.4^2\newline 0.4^2,& 0.4^2,& 0.4^2\end{bmatrix}$
SCP forces:
DDP tracking SCP forces:
Pybullet monte-carlo simulations:
I ran 100 monte-carlo simulations while adding a sampled random forces from the covariance of the linear momentum at the center of the robot base, then checked if the contact forces from pybullet is inside the friction cone constraints.
no. of constraint violations from DDP tracking nominal SCP = 20183 no. of constraint violations from DDP tracking stochastic SCP = 14630 avg. cost nominal = 1.807048631332169 avg. cost stochastic = 2.022525420858646
Bound motion
dt = 0.01 Gait parameters = {'stepLength' : 0.1, 'stepHeight' : 0.1, 'stepKnots' : 10, 'supportKnots' : 15, 'nbSteps': 3}
Covariance of the additive white noise on centroidal dynamics $\Sigma_w = \begin{bmatrix} 0.6^2,& 0.3^2,& 0.3^2 \newline 0.9^2,& 0.3^2,& 0.3^2\newline 0.9^2,& 0.4^2,& 0.3^2\end{bmatrix}$
Covariance of the contact position noise $\Sigma_p = \begin{bmatrix} 0.4^2, &0.4^2,& 0.4^2 \newline 0.4^2,& 0.4^2,& 0.4^2 \newline 0.4^2,& 0.4^2,& 0.4^2 \end{bmatrix}$
SCP forces:
DDP tracking SCP forces:
Pybullet monte-carlo simulations:
no. of constraint violations from DDP tracking nominal SCP = 33376 no. of constraint violations from DDP tracking stochastic SCP = 32770 avg. cost nominal = 1.303355238919714 avg. cost stochastic = 1.314369381557627