Abstract：A modified nonlinear model predictive control(NMPC)strategy is proposed for the realtime gait programming problem of biped robot.Extended joint coordinates are used to represent both the single support phase(SSP)and the double support phase(DSP)as an identical nonlinear dynamical model.Through setting kinetic and kinematic virtual constraints to SSP and the three sub-phases of DSP,the complex realtime gait programming problem is transformed into four NMPC problems which use the quadratics of inputs in the predictive horizon as the cost functions.Direct method is used to parame- terize the continuous optimization problem as a finite dimensional optimization problem,penalty function method is used to transform the state constraints into the penalty items in cost function,and the finite dimensional static optimization problem which can be solved with sequential quadratic programming(SQP)is acquired.Simulation has been made to use the pre- sented method to implement realtime gait programming of BIP robot,and the results show that dynamic walking(including foot rotation)is realized,and biped stability is satisfied without any side slipping.So effectiveness and applicability of the presented approach are verified.
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