Legged robots have enormous potential to automate dangerous or dirty jobs because they are capable of traversing a wide range of difficult terrains such as up stairs or through mud. However, a significant challenge preventing widespread deployment of legged robots is a lack of robust state estimation, particularly in visually challenging conditions such as darkness or smoke.

In this thesis, I address these challenges by exploiting proprioceptive sensing from inertial, kinematic and haptic sensors to provide more accurate state estimation when visual sensors fail. Four different methods are presented, including the use of haptic localisation, terrain semantic localisation, learned inertial odometry, and deep learning to infer the evolution of IMU biases.

The first approach exploits haptics as a source of proprioceptive localisation by comparing geometric information to a prior map. The second method expands on this concept by fusing both semantic and geometric information, allowing for accurate localisation on diverse terrain.

Next, I combine new techniques in inertial learning with classical IMU integration and legged robot kinematics to provide more robust state estimation. This is further developed to use only IMU data, for an application entirely different from robotics:​ 3D reconstruction of bone with a handheld ultrasound scanner. Finally, I present the novel idea of using deep learning to infer the evolution of IMU biases, improving state estimation in exteroceptive systems where vision fails.

Legged robots have the potential to benefit society by automating dangerous, dull, or dirty jobs and by assisting first responders in emergency situations. However, there remain many unsolved challenges to the real-world deployment of legged robots, including accurate state estimation in vision-denied environments. The work presented in this thesis takes a step towards solving these challenges and enabling the deployment of legged robots in a variety of applications.