Symbolic analysis of the base parameters for closed-chain robots based on the completion procedure

Parameter identification of robotic systems with series elastic actuators

“…To facilitate estimation of the model parameters, the system model should be written in the so-called regressor form, Gautier and Khalil [1988], Kawasaki et al [1996], Calafiore et al [2001], Waiboer et al [2005]:…”

“…where ζ ∈ R n is a vector of parameter independent expressions, R (q,q,q) ∈ R n×m is the regressor matrix, ϑ ∈ R m is a vector of unknown parameters, n is the number of the robot links, and m is the number of unknown parameters. For reliable system identification, the columns of the regressor matrix must be linearly independent, which is the so-called base regressor form, Khalil [1989, 1990], Kawasaki et al [1996]. In the following, subscript 0 will be used to denote the base regressor form.…”

“…To facilitate automatic conversion Algorithm 1. Regression algorithm for r ← 1, n do e ← str(eom (r)) pmop ← sort( [ strfind(e, '+') , strfind(e, '-') ] ) for i ← 1, len(pmop) − 1 do pms ← e (pmop (i) + 1 : of the regressor form (9) into the base regressor form, the reasoning proposed in Kawasaki et al [1996] can be used. The regressor matrix R contains expressions that are time-varying functions of joint variables and their timederivatives.…”

“…Hence, in this paper we contribute a systematic method to model and estimate geometric and inertial parameters of such robotic systems. Unlike a common way to identify series elastic actuation using static measurements, in this paper we propose a dynamic system identification, Calafiore et al [2001], Kawasaki et al [1996], using a regressor form of a model of the series elastic actuation. Our method offers a more efficient identification than static measurements, since it estimates parameters of actuator, drive train and load at once with only one set of experimental data.…”

Model parameter estimation of humanoid robots using static contact force measurements

“…Rewriting (4) to (6) can be difficult especially when the equations are very large, as is the case for a humanoid robot with twelve joints. However, in [11] we have developed an automatic algorithm based on [22] to accomplish this task. Moreover, the BPS is not unique, parameters may be grouped differently to improve the final identification results.…”