Abstract—This paper introduces a state estimation framework for legged robots that allows estimating the full pose of the robot without making any assumptions about the geometrical structure of its environment. This is achieved by means of an Observability Constrained Extended Kalman Filter that fuses kinematic encoder data with on-board IMU measurements. By including the absolute position of all footholds into the filter state, simple model equations can be formulated which accurately capture the uncertainties associated with the intermittent ground contacts. The resulting filter simultaneously estimates the position of all footholds and the pose of the main body. In the algorithmic formulation, special attention is paid to the consistency of the linearized filter: it maintains the same observability properties as the nonlinear system, which is a prerequisite for accurate state estimation. The presented approach is implemented in simulation and validated experimentally on an actual quadrupedal robot. I
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