Gradient-Based Pose Tracking Law on SE(3) in Unknown Environment

When inertial information is unavailable to locate the inertial reference frame, i.e., the environment is unknown, it is usually difficult to conduct pose tracking tasks for rigid bodies. To address this problem, based on the adopted pose observer, we can determine an estimated reference frame from the estimates. Then we express the desired pose trajectory with respect to the estimated frame and develop a gradient-based pose tracking law on SE(3) to deal with relative pose trajectory tracking. The dynamics of the combined observer-controller are analyzed, rigorously showing almost global asymptotic stability of the combination. Simulations are also conducted to show the effectiveness of our method.