  Sampling-based model predictive control (MPC) can be applied to versatile
robotic systems. However, the real-time control with it is a big challenge due
to its unstable updates and poor convergence. This paper tackles this challenge
with a novel derivation from reverse Kullback-Leibler divergence, which has a
mode-seeking behavior and is likely to find one of the sub-optimal solutions
early. With this derivation, a weighted maximum likelihood estimation with
positive/negative weights is obtained, solving by mirror descent (MD)
algorithm. While the negative weights eliminate unnecessary actions, that
requires to develop a practical implementation that avoids the interference
with positive/negative updates based on rejection sampling. In addition,
although the convergence of MD can be accelerated with Nesterov's acceleration
method, it is modified for the proposed MPC with a heuristic of a step size
adaptive to the noise estimated in update amounts. In the real-time
simulations, the proposed method can solve more tasks statistically than the
conventional method and accomplish more complex tasks only with a CPU due to
the improved acceleration. In addition, its applicability is also demonstrated
in a variable impedance control of a force-driven mobile robot.
https://youtu.be/D8bFMzct1XM
