Parallel force/position controllers for robot manipulators with uncertain kinematics

Force control is crucial for successful execution of a number of practical tasks. Parallel force/position control is an attractive approach for robot force regulation, although several force control strategies, such as stiffness control, impedance control, and hybrid force/position control, have been developed. Unfortunately, the existing theoretic works on parallel force/position control scheme deal only with linear mechanical characteristics and planar constraints (environment), and in addition require exact robot kinematics. Under the condition of uncertain robot kinematics (or Jacobian matrix), this paper develops parallel force/position controllers without gravity compensation and desired force feedforward; stability of the resulting system is rigorously analyzed in the presence of nonlinear mechanical characteristics of environment and nonplanar surface constraints instead of linear mechanical characteristics and planar constraints addressed in the existing work. We show that asymptotic stability of set-point force regulation is guaranteed when some assumptions are satisfied. In some sense, this result reveals some robustness of parallel force/position control scheme to uncertain environment including geometry and mechanical characteristics. In the case of imperfect force planning, the resulting closed-loop system has constant stead solution instead of an equilibrium trajectory if force-regulation solvability assumption is satisfied. Lastly, with comparisons to hybrid force/position control scheme, numerical simulation demonstrates the effectiveness and performance of the resulting closed-loop system.