In constrained motion control of a robot, the interaction force is an important variable, which directly describes the state of interaction. It is required in a number of algorithms for interaction control. Desirably, the interaction force has to be measured by force sensors. However, there are inherent limitations with force sensors, such as the cost, sensing noise, limited bandwidth, and the difficulty of physical location at the required place, which is dynamic. In the present paper, the interaction force is estimated by using high order sliding mode observers. An adaptive version of a high order sliding mode observer is developed to robustly reconstruct the interaction force. Experimental results are given to show the effectiveness of the developed algorithms.