Real Time Optimization for Robot Control using Receding Horizon Control with Equal Constraint

Abstract

Abstract The equation to define a legged robot's ZMP (zero moment point) suggests a problem that ZMP cannot be obtained uniquely. This is because a redundancy exists in the equation which defines ZMP. Obtaining a true ZMP requires optimization calculation and this took a very long calculation time. We have to execute off‐line optimization beforehand. Then a real‐time control system follows these optimum trajectories which satisfy the ZMP condition. This is inconvenient for real‐time control of a robot. Carrying out a reduction of the equation so that it uniquely defines ZMP may assist in temporarily avoiding this problem. However, a pseudo ZMP is only able to be found. On the other hand, since RHC (receding horizon control), which is the new optimization technique, does not use a gradient method for optimization calculation, then it requires very little calculation time. This short time calculation such as sampling interval makes it possible to perform a real‐time calculation. However, RHC has not yet been applied to robot control. If an equality constraint can be set up in the formulation of RHC, it will be easy to apply to robot control. In this paper, it is proposed that RHC is used adding an equality constraint and then the formulation is performed. We discuss that the ZMP condition is used in the formulation using an equality constraint. Generally, it is difficult to take a ZMP variable as a state variable in a state equation. To ensure an optimal result, careful consideration of the ZMP conditions is required for the formulation. Then, this paper shows that the ZMP is defined as one of the input variables. Since ZMP input is obtained as an optimal solution, the technique proposed can generate a true ZMP trajectory on real time. Simulation results are performed by both the models in a two‐dimensional plane and the three‐dimensional space. This simple modeling enables an easy application to biped, quadruped and the other multiped robots. This simple modeling forms a basis for robot control. © 2003 Wiley Periodicals, Inc.