On Force Tracking Impedance Control with Unknown EnvironmentSti ness

In impedance control for contact force tracking, it is well known that the reference trajectory of the robot is calculated from known environment stiiness 1]. Here we present a simple technique for determining the reference trajectory under the condition that the environment stiiness is unknown. The technique is developed based on the replacement of the unknown stiiness with a function of the measured contact force. The design technique is shown to be robust in the presence of sensor noise. Computer simulation studies have demonstrated that force tracking using the proposed technique is excellent for unknown environment stiiness. The practicality of the technique is also veriied experimentally using a PUMA 560 manipulator. The impedance control technique proposed by Hogan has been one of the fundamental approaches for force tracking control of robot manipulators with constrained motion. Unlike the hybrid position and force control approach 2], impedance control regulates the contact force of a manipulator with the environment by the target impedance between position and contact force. The desired contact force is indirectly controlled by prespecifying a robot positional reference trajectory which is determined based on the stiiness and location of the environment. One of the major practical diiculties with this technique is that the environment stiiness is usually not known precisely so that accurate reference trajectory can not be designed to achieve accurate contact force control. The other problem is the design of robust robot position controllers to accurately track the reference trajectory in the presence of robot dynamics uncertainties. There have been many attempts made in the past to solve the problem of unknown environment stii-ness such as by employing separate reference trajec-tory modiication control loop using integral control 3], or by generating reference position using adaptive control 4, 5]. Although these techniques are shown to work, they tend to increase the complexity of the system dynamics which requires special attention to system stability. In this paper we propose a simple technique for reference trajectory design in the case when environment stiiness is assumed unknown. The design makes use of the contact force information, which can be measured using force sensors, instead of environment stii-ness since they are directly related. Consequently, the design approach is able to provide reference trajecto-ries for unknown and arbitrarily varying environment stiinesses. This capability is of great practical interests as a given environment may exhibit non-uniform stiiness along the path of contact. The reference trajectory …