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Block diagram of the observer 

Block diagram of the observer 

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... architecture of the observer is summarized in Fig. 2. Implementation details are presented in the following subsections. ...

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Citations

... Piperakis et al. (Piperakis & Trahanias, 2016) used nonlinear dynamics of CoM as process model to estimate three-dimensional external force based on extended Kalman filter (EKF), and improved the accuracy by considering the influence of the rate of angular momentum in Piperakis et al. (2018). To simplify the observer and make it easy to run in real-time with the embedded processor of low-cost biped robots, Hawley et al. (Hawley & Suleiman, 2016) explored the relationship between external force and ZMP, and fused the measurements from IMU and FSRs to estimate the external force. The model of the observer is linear, thus the filter is implemented by simple KF. ...
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... where c L , c R , n L and n R are the measured CoP and GRF using sensor parameters solved by (19) for the left and right feet. ∆s L and ∆s R are the correction terms applied to the left and right feet defined in (5). Then we use NLS to minimize the error between corrected and modeled CoPs over the parameters of the correction terms: ...
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... Another model-based method to estimate the magnitude of an external force applied to a humanoid robot is presented in [16]. Its main advantage is that it does not require using F/T sensors but instead it uses measurements from the robot's force-sensing resistors (FSR) sensors. ...
... where 2 ... z c and 2F z are respectively the covariance of ... z c andF z . By applying Kalman filter on (16), an estimation of the state vector is obtained: ...
... CoM Acceleration ZMP CoM position Ground reaction force Kalman filter applied on Eq (16) z c (kT ) ...
... Another model-based method to estimate the magnitude of an external force applied to a humanoid robot is presented in [16]. Its main advantage is that it does not require using F/T sensors but instead it uses measurements from the robot's force-sensing resistors (FSR) sensors. ...
... where 2 ... z c and 2F z are respectively the covariance of ... z c andF z . By applying Kalman filter on (16), an estimation of the state vector is obtained: ...
... CoM Acceleration ZMP CoM position Ground reaction force Kalman filter applied on Eq (16) z c (kT ) ...
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... where σ 2 ... z c and σ 2F z are respectively the covariance of ... z c andF z . By applying Kalman filter on (16), an estimation of the state vector is obtained: ...
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... where the operators × and (.|.) design respectively the cross and scalar products, and 1 As a general rule, bold parameters are vectors or matrices ...
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... In a previous work [7], we proposed a method to estimate an external force applied in the horizontal plane. This method is mainly designed for small humanoid robots, such as Nao robot, and only uses the information from Force Sensitive Resistors (FSR) and Inertial Measurement Unit (IMU). ...
... In order to estimate the parameters of the cart, three experiments were performed with a Nao robot pushing different masses using a rudimentary wheeled-table. In each experiment, we estimated the external force applied on the robot using our force observer [7], and tried to correctly guess the mass transported on the cart by using Eq. (3) and varying the cart-parameter µ. ...
... • A mass of 5kg is then added on the cart at T = T 0 while the robot continues to walk as usual. • The robot estimates the mean of detected external forces over an interval of 4 steps (about 3 seconds) [7]. • At T = T 0 + 5s, the robot controller is triggered manually and the transported mass is estimated using Eq.(3), and then integrated into the walk pattern generator using the control law presented in Section III. ...