When a robot arm performs a hybrid task, it applies specified forces to a fixed surface or mechanism while moving along a prescribed path. To control simultaneously the contact force and the arm position, three generic feedback control schemes have been proposed in the literature. This thesis investigates the stability of these 'hybrid controls' in the presence of joint compliance and contact compliance. While it is well known that compliance produces instability in robots that use force feedback, it is shown in this thesis that compliance can destabilize certain hybrid control even when force feedback is not used. First it is proved that each hybrid control is exponentially stable when no compliance is present. Then two of the controls are shown to be unstable when compliance is introduced, while the third control is proved exponentially stable with joint compliance, contact compliance or both sources present. A novel hybrid control is proposed that achieves exponential tracking when applied to rigid systems as well as exponential stability in the presence of compliance. A general theoretical connection is made between exponential stability and trajectory tracking. The concept of hybrid control is demonstrated on a 3-degree-of-freedom experimental manipulator performing a writing task.

The stability analyses presented in this thesis pertain to robots in contact with arbitrary holonomic constraints. It is shown that Raibert and Craig's established method for hybrid task specification applied to only a subset of these constraints. Theoretical justification is provided for Yoshikawa's more general method for specifying hybrid tasks. This development effectively extends to scope of previously proposed hybrid controls to arbitrary holonomic constraints. It is proved that one of these hybrid controls is identical to a control proposed by McClamroch and Wang for holonomically constrained robots.