  Control techniques like MPC can realize contact-rich manipulation which
exploits dynamic information, maintaining friction limits and safety
constraints. However, contact geometry and dynamics are required to be known.
This information is often extracted from CAD, limiting scalability and the
ability to handle tasks with varying geometry. To reduce the need for a priori
models, we propose a framework for estimating contact models online based on
torque and position measurements. To do this, compliant contact models are
used, connected in parallel to model multi-point contact and constraints such
as a hinge. They are parameterized to be differentiable with respect to all of
their parameters (rest position, stiffness, contact location), allowing the
coupled robot/environment dynamics to be linearized or efficiently used in
gradient-based optimization. These models are then applied for: offline
gradient-based parameter fitting, online estimation via an extended Kalman
filter, and online gradient-based MPC. The proposed approach is validated on
two robots, showing the efficacy of sensorless contact estimation and the
effects of online estimation on MPC performance.
