We present an algorithm, based on the Differential Dynamic Programming framework, to handle trajectory optimization problems in which the horizon is determined online rather than fixed a priori. This algorithm exhibits exact one-step convergence for linear, quadratic, time-invariant problems and is fast enough for real-time nonlinear model-predictive control. We show derivations for the nonlinear algorithm in the discrete-time case, and apply this algorithm to a variety of nonlinear problems. Finally, we show the efficacy of the optimal-horizon model-predictive control scheme compared to a standard MPC controller, on an obstacle-avoidance problem with planar robots.
翻译:我们根据不同动态编程框架提出一种算法,处理轨道优化问题,其中地平线是在线确定的,而不是先验地固定的。这种算法显示了线性、二次、时间变化性问题的一步趋同性,对于实时的非线性模型预测性控制来说足够快。我们展示了离散时非线性算法的衍生结果,并将这种算法应用于各种非线性问题。最后,我们展示了与标准的MPC控制器相比,最佳偏差模型预测性控制方案的效力,它涉及平板机器人的避免障碍问题。