Reduction of the On‐line Measurement and Control Expenses by Adaptive Stochastic Path Planning

Abstract

In the optimal control of dynamic systems, e.g., in the control of industrial or service robots, the standard procedure is to determine first off-line an optimal open loop control, and correct then the inevitable deviation of the trajectory 01' performance of the system from the prescribed values b y on-line measurement and control actions which may be very expensive. By adaptive stochastic path planning and control (ASPPC), i. e. b y incorporating the available a priori and statistical information on the unknown model parameters of the dynamic system and its working environment into the off-line and on-line control process by means of stochastic optimization methods , the deviation between the actual and prescribed trajectory can be reduced to a large extent. s 100 Now, the following statement about the behaviour of the error vector A z ( t ) , t 2 t j , can be made: robotic system described by (15a116) and A(j)z(t) := E ( A z ( t ) I At,). Then ZAMM . Z. Angew. Math. Mech. 80 (2000) S1 T h e o r e -m 5.1. Let A z = A z ( t ) , t > t j , be the first order expansion term of the tracking error of the t t However, in (OSPP) the following control restrictions are used U m i n ( P C , s ) 5 u g ( P D i S ; i ( . ) l P ( . ) ) 5 umaz(PC,s), s j 5 s 5 S f . Having an (OSPP) with reliability conditions and using (3), (17) is replaced by Finally, comparing Theorem 5.1 and (20) we obtain:T h e o r e m 11.2. By using optimal stochastic path planning (OSPP), the variance of the tracking error A z ( t ) is minimized. Therefore more stable controls are obtained and the expense for on-line corrections is reduced. 6. References 1 MARTI, K.: Path planning for robots under stochastic uncertainty; Optimization 1999,to appear. 2 MARTI, K., Qu, S.: Path planing for robots by stochastic optimization methods; Preprint 97-12, DFG reasearch project 3 Q u , S.: Optimale Bahnplanung fur Roboter unter Berucksichtigung stochastischer Parameterschwankungen; VDI-Verlag, Echtzeit Optimierung grosser Systeme, 1997. Dusseldorf 1995.