Observer/Controller With Global Practical Stability for Tracking in Robots Without Velocity Measurement

Abstract

In this work, a global practical stability (GPS) observer/controller is given for a revolute-jointed multiple degree of freedom robotic plant without velocity measurement and without knowledge of plant parameter values and with a globally bounded disturbance torque. For this considered plant, a global observer/controller that globally drives the combined estimation and position tracking error to a set on which the tracking error can be made arbitrarily small by adjusting parameters/gains of the observer/controller is proposed. For the above-mentioned plant, the current paper is the first GPS result for which the control torque is not an exponential function of a (filtered) tracking error. This paper is also the first global result for which the convergence to the residual set is exponential in time (Global Exponential Practical Stability). The observer update is discontinuous, however, only at isolated time instants. No sliding modes are used. Also, the torque is continuous.

Decentralized Observer Design for Virtual Decomposition Control

“…3]. The joint dynamics are given in line with (15) by I m,iqi = τ i − τ ai − f c,i (q i ), where I m,i = 0.1 and f c,i (q i ) = tanh(q i ) for i ∈ {1, 2}. Finally, τ i is the input torque for joint i and τ ai is given by (14).…”

“…Velocity data can naturally be obtained by numerical differentiation of the position sensor data but there is no theoretical justification for this method [8], [9]. Due to these challenges, control of n-DoF robotic manipulators without velocity data has been extensively studied, e.g., in [8], [10]- [15], see also the survey [9], where the actuator dynamics have been neglected. Similar research for robots with, e.g., hydraulic actuators has been done in [16], [17].…”

Decentralized Observer Design for Virtual Decomposition Control

“…Single Link Dynamics in Cartesian Space. As in (5), the motion dynamics of a rigid link i ∈ {1, 2, . .…”

“…Velocity data can naturally be obtained by numerical differentiation of the position sensor data but there is no theoretical justification for this method [2,3]. Due to the these challenges, control of n-DoF robotic manipulators without velocity data has been extensively studied, e.g., in [2,4,5,10,14], see also the survey [3], where the actuator dynamics have been neglected. Similar research for robots with, e.g., hydraulic actuators has been done in [6,12].…”