This paper considers the use of two position receivers and an inertial measurement unit (IMU) to estimate the position, velocity, and attitude of a rigid body, collectively called extended pose. The measurement model consisting of the position of one receiver and the relative position between the two receivers is left invariant, enabling the use of the invariant extended Kalman filter (IEKF) framework. The IEKF possesses various advantages over the standard multiplicative extended Kalman filter, such as state-estimate-independent Jacobians. Monte Carlo simulations demonstrate that the two-receiver IEKF approach yields improved estimates over a two-receiver multiplicative extended Kalman filter (MEKF) and a singlereceiver IEKF approach. An experiment further validates the proposed approach, confirming that the two-receiver IEKF has improved performance over the other filters considered.

This paper considers modeling and control of a planar flexible two-link telescoping manipulator. The telescoping interface between the deploying and non-deploying portions of the links is discussed in detail. The equations of motion are derived using Lagrange's equation and constrained using a projection method that eliminates the need to compute Lagrange multipliers explicitly. Passivity-based control of the telescoping manipulator is also investigated. It is shown that several passive input-output maps exist. In particular, by a suitable redefinition of the inputs and outputs, a modified tip-based control is made possible. The model is validated through numerical simulation, and the tip-based control is compared with joint-based control. Simulation results show that tip-based control has better closed-loop performance compared with joint-based control.