Kalman Filter Based Observer for an External Force Applied to Medium-sized Humanoid Robots

Abstract

External force observer for humanoid robots has been widely studied in the literature. However, most of the proposed approaches generally rely on information from sixaxis force/torque sensors, which the small or medium-sized humanoid robots usually do not have. As a result, those approaches cannot be applied to this category of humanoid robots, which is widely used nowadays in education or research. In this paper, we improve the external force observer in [1] to handle the case of an external force applied in any direction and at an arbitrary point of the robot structure. The new observer is based on Kalman filter formulation and it allows the estimation of the three force components. The observer is simple to implement and can easily run in real time using the embedded processor of a medium-sized humanoid robot such as Nao or Darwin-OP. Moreover, the observer does not require any change to the robot hardware as it only uses measurements from the available force-sensing resistors (FSR) inserted under the feet of the humanoid robot and from the robot inertial measurement unit (IMU). The proposed observer was extensively validated on a Nao humanoid robot. In all conducted experiments, the observer successfully estimated the external force within a reasonable margin of error.

Control framework for cooperative object transportation by two humanoid robots

“…As shown in [2,13], the ZMP is given by the following formula (for more details, refer to Appendix A):…”

“…reduction ratio). Compared to our observer [13], the motor error signal (q d − q) is less noisy, and more importantly only detects the forces that are applied to the robot hands. However, as pointed out in [24], the error signal is only meaningful with a large interaction force that produces a relatively high signal to noise ratio.…”

“…K p1 and K p2 are proportional gains and IK stands for Inverse Kinematics algorithm that converts the shoulder displacement (q) into an equivalent hand displacement (∆x h ), the aim being to move the shoulders while keeping the hands in a parallel plane with respect to the floor. The secondary component is a feedforward compensation that is computed using the output from our external force observer [13], F x . The estimated force F x is converted into a relative hands displacement (∆x h 2 ) using a proportional gain and injected into the main loop.…”

“…The performance of the compliance controller was validated by a springbased force sensor as well as by our external force observer [13]. As shown in Fig.…”

“…To this end, we used the external force observer described in [13]. The transported mass could then be directly estimated using the observed force along the vertical axis, F z , as follows: rigid table.…”