Human–Robot co-manipulation during surface tooling: A general framework based on impedance control, haptic rendering and discrete geometry

•A surface-constrained object (proxy) is used 1) to capture the local geometry of a free-form surface and 2) to allow for Realtime impedance-control of a robot.•b) This framework, by setting a few parameters, can be used to account for scenarios such as 1) Proxy assisted simulated robot navigation avoids the obstacles in the path 2) Proxy, driven by a force, traces a geodesic trajectory in the direction of the force 3) Motion constraints, imposed on a proxy, minimize human error in collaborative tasks.•Our proxy-based robot-surface interaction framework requires minimal end-user programming.