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Stable estimation of rigid body pose and velocities from noisy measurements,without any knowledge of the dynamics model, is treated using theLagrange-d'Alembert principle from variational mechanics. With body-fixedoptical and inertial sensor measurements, a Lagrangian is obtained as thedifference between a kinetic energy-like term that is quadratic in velocityestimation error and the sum of two artificial potential functions; oneobtained from a generalization of Wahba's function for attitude estimation andanother which is quadratic in the position estimate error. An additionaldissipation term that is linear in the velocity estimation error is introduced,and the Lagrange-d'Alembert principle is applied to the Lagrangian with thisdissipation. This estimation scheme is discretized using discrete variationalmechanics. The presented pose estimator requires optical measurements of atleast three inertially fixed landmarks or beacons in order to estimateinstantaneous pose. The discrete estimation scheme can also estimate velocitiesfrom such optical measurements. In the presence of bounded measurement noise inthe vector measurements, numerical simulations show that the estimated statesconverge to a bounded neighborhood of the actual states.

Rigid Body Motion Estimation based on the Lagrange-d'Alembert Principle