CARTESIAN SLIDING PD FORCE-POSITION CONTROL FOR CONSTRAINED ROBOTS UNDER JACOBIAN UNCERTAINTY V. Parra-Vega ∗,1,2 R. Garc´ ıa-Rodr´ ıguez, F.Ruiz-Sanchez ∗,2 ∗ Mechatronics Division, CINVESTAV - IPN AP 14-740, M´ exico, D.F., 07300 M´ exico . Abstract: Joint control requires to map, using ill-posed inverse kinematics, desired cartesian tasks into desired joint tasks, then it codes them into desired joint trajectories. To avoid this, cartesian control directly codes the cartesian task in cartesian coordinates, avoiding in this way any computation of inverse kinematics, which is relevant in particular for force control since the force task is always given in operational (cartesian) space. In this paper, a local cartesian exponential tracking control for constrained motion without using inverse kinematics is proposed. The novelty lies, besides its nontrivial extension from ODE (position) robots to DAE (force) robots, in the fact that fast cartesian tracking is obtained without using the model of the robot nor exact knowledge of inverse jacobian. The scheme shows a smooth control input. Simulations results shows the expected tracking performance. Copyright c  2005 IFAC Keywords: Force Control, Cartesian Control, Second Order Sliding Mode, Robot Manipulators 1. INTRODUCTION Mode-based inverse dynamics (with and with- out coordinate partitioning, (McClamroch and Wang, 1998) , (Parra-Vega and Arimoto, 1996), respectively), and adaptive joint control for con- strained system yield the simultaneous asymp- totic convergence of position and force tracking errors, while the first order sliding mode control produce exponential tracking at the expense of chattering, whose discontinuity renders a high fre- quency controller that is impossible to implement in practice (Parra-Vega and Hirzinger, 2001). 1 Partially supported by CONACYT project 39727-Y 2 Email:(vparra,rgarciar,fruiz)@cinvestav.mx To implement a joint robot control, the desired joint reference is computed from desired carte- sian coordinates using inverse mappings and its derivatives up to second order. The main difficulty of computing inverse kinematics is represented by the fact of the ill-posed nature of the inverse kinematic mappings. In contrast, cartesian con- trol does not require inverse kinematics mappings since it accepts directly desired cartesian coordi- nates. This saving is significant in real time ap- plications because inverse kinematics are hard to compute on line. So, cartesian control arises as an option to circumvent the computation of inverse kinematics, and this is the subjacent interest of this scheme. Solving this problem would allow to design efficient and intuitive to tune controllers with very low computational cost.