A Screw Representation for Attitude Estimation and Its Application to Legged Locomotion

Efficient motion estimation is central to observing and controlling dynamic legged locomotion. This paper considers a screw-theoretic (line-oriented) representation for this context and illustrates this on the attitude estimation subproblem. This is presented as part of an Extended Kalman Filter (EKF) based on inertial (gyroscopic) sensing in which each measurement axis is treated as an zeropitch, instantaneous screw axis. The implemented solution integrates this to tracks both the orientation and the body screw-axis. In comparison to point-oriented (quaternion) representations, this method is more general, computationally efficient, and provides a more intuitive mechanism for specifying motion constraints, especially for rotary joint motion(s) such as those that at the foot. This technique is demonstrated on a trotting quadrupedal robot at a 250 Hz rate and with drift errors limited to a 5◦ bound.