基于双生成函数的步行机器人最优步态生成

将最优控制理论中的双生成函数方法应用到双足步行机器人的在线最优步态生成中.针对线性化的机器人模型，分别以关节角度和力矩为状态和输入变量，考虑能量消耗，构造线性二次型最优控制问题.基于一对生成函数推导得到该问题的解，可以参数化为线下计算系数和边界条件，相对应的求解过程由线下数值积分部分和线上代数运算部分组成.通过设置多步仿真实例进行计算.结果表明，利用该方法可以显著地提高机器人步态的在线生成效率.设计比例微分控制器，当机器人以合理的步长和适当的时间段行走时，由线性化引起的建模误差可以被控制在较小范围之内，非线性模型的轨迹可以很好地跟踪线性化模型的轨迹.

On-line optimal gait generation for biped walking robot by using double generating functions method

The double generating functions method from optimal control theory was applied to the on-line optimal gait generation of the biped walking robot.A linear quadratic optimal control problem was designed for the linearized robot model by taking the joint angle and torque as state and input variables respectively and considering its energy consumption.The solution of the problem was derived based on a couple of generating functions,and can be parametrized as the off-line calculated coefficients and boundary conditions. The evaluation correspondingly consisted of the off-line numerical integration part and on-line algebraic computation part.A multi-step example illustrated that the method promoted the efficiency of the on-line trajectory generation.Then a PD controller was designed. When the robot walks with reasonable step lengths and time periods,the error induced by the linearization can be controlled within a small range that the trajectory of the nonlinear model can well follow the reference trajectory of the linearized model.