This paper suggests a Kalman-filter approach to the estimation of angular velocity and acceleration from (quantized) shaft-encoder measurements. Finite-difference estimates deteriorate as sampling rates are increased. For small sampling periods, we show that the filtering problem is the dual of the cheap control problem, and we jus tify the use of all-integrator models. We investigate Kalman filtering with constant sampling rate, and also with measurements triggered by encoder pulses. Simulation and experimental results are given.
Get full access to this article
View all access options for this article.
References
1.
An, C.H., Atkeson, G.C., Christopher, J.M., and Hollerbach, J.M.1985 (Fort Lauderdale, FL). Estimation of inertial parameters of rigid-body links of manipulators. Proc. of the IEEE Conf. on Decision and Control. Los Alamitos, CA: IEEE.
2.
Bélanger, P.R.1991. Estimation of angular velocity and acceleration from shaft-encoder measurements. Technical Report TR-CIM-91-1, McGill Research Center for Intelligent Machines. (Also Technical Report 1436, INRIA.)
3.
Bierman, G.1977. Factorization Methods for Discrete Estimation. New York: Academic.
4.
Brown, R.H., Schneider, S.C., and Mulligan, M.G.1992. Analysis of algorithms for velocity estimation from discrete position vs. time data. IEEE Trans. Indust. Electronics39:11-19.
5.
Canudas deWit, C., and Fixot, N.1991. Robot control via estimated state feedback. IEEE Trans. Automat. Control36:1497-1501
6.
Dunworth, A.1969. Digital instrumentation for angular velocity and acceleration . IEEE Trans. Instr Meas.18:132-138
7.
Friedland, B.1971. Limiting forms of optimum stochastic linear regulators . J. Dyn. Syst. Meas. Control93:134-141.
8.
Glad, T., and Ljung, L.1984 (Budapest). Velocity estimation from irregular, noisy position measurements. Proc. of the IFAC 9th World Congress. IFAC .
9.
Habibullah, B., Singh, H., Soo, K.L., and Ong, L.C.1978. A new digital speed transducer. IEEE Trans. Ind. Electron. Control Instr.25:339-343.
10.
Harrison, A.J., and McMahon, C.A.1993. Estimation of acceleration from data with quantization errors using control finite-difference methods. Proc. Inst. Mech. Engineers207:77-86.
11.
Kailath, T.1980. Linear Systems. Prentice Hall Inc.
12.
Luo, G.L., and Saridis, G.N.1985. L-Q design of PID controllers for robot arms. IEEE J. Robot. Automat.1:152-158.
13.
Nicosia, S., and Tomei, P.1990. Robot control by using only joint position measurements . IEEE Trans. Automat. Control35:1058-1061.
14.
Sinha, N.K., Szavados, B., and di Cenzo, D.C.1971. New high- precision digital tachometer. Electronics Lett.7:174-176.
15.
Studenny, J., and Bélanger, P.R.1986 (Athens). Robot manipulator control by acceleration feedback: Stability, design, and performance issues. Proc. of the 25th IEEE Conf. on Decision and Control. Los Alamitos, CA: IEEE.
16.
Wallingford, E.E., and Wilson, J.D.1977. High-resolution shaft-speed measurements using a microcomputer . IEEE Trans. Instr. and Meas.26:113-116.
