  Controlling contacts is truly challenging, and this has been a major hurdle
to deploying industrial robots into unstructured/human-centric environments.
More specifically, the main challenges are: (i) how to ensure stability at all
times; (ii) how to satisfy task-specific performance specifications; (iii) how
to achieve (i) and (ii) under environment uncertainty, robot parameters
uncertainty, sensor and actuator time delays, external perturbations, etc.
Here, we propose a new approach -- Convex Controller Synthesis (CCS) -- to
tackle the above challenges based on robust control theory and convex
optimization. In two physical interaction tasks -- robot hand guiding and
sliding on surfaces with different and unknown stiffnesses -- we show that CCS
controllers outperform their classical counterparts in an essential way.
