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Register a new userOptimal Cost Design for Model Predictive Control
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Added by
Daniel Brown
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Many robotics domains use some form of nonconvex model predictive control (MPC) for planning, which sets a reduced time horizon, performs trajectory optimization, and replans at every step. The actual task typically requires a much longer horizon than is computationally tractable, and is specified via a cost function that cumulates over that full horizon. For instance, an autonomous car may have a cost function that makes a desired trade-off between efficiency, safety, and obeying traffic laws. In this work, we challenge the common assumption that the cost we optimize using MPC should be the same as the ground truth cost for the task (plus a terminal cost). MPC solvers can suffer from short planning horizons, local optima, incorrect dynamics models, and, importantly, fail to account for future replanning ability. Thus, we propose that in many tasks it could be beneficial to purposefully choose a different cost function for MPC to optimize: one that results in the MPC rollout having low ground truth cost, rather than the MPC planned trajectory. We formalize this as an optimal cost design problem, and propose a zeroth-order optimization-based approach that enables us to design optimal costs for an MPC planning robot in continuous MDPs. We test our approach in an autonomous driving domain where we find costs different from the ground truth that implicitly compensate for replanning, short horizon, incorrect dynamics models, and local minima issues. As an example, the learned cost incentivizes MPC to delay its decision until later, implicitly accounting for the fact that it will get more information in the future and be able to make a better decision. Code and videos available at https://sites.google.com/berkeley.edu/ocd-mpc/.
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Mars has been a prime candidate for planetary exploration of the solar system because of the science discoveries that support chances of future habitation on this planet. Martian caves and lava tubes like terrains, which consists of uneven ground, poor visibility and confined space, makes it impossible for wheel based rovers to navigate through these areas. In order to address these limitations and advance the exploration capability in a Martian terrain, this article presents the design and control of a novel coaxial quadrotor Micro Aerial Vehicle (MAV). As it will be presented, the key contributions on the design and control architecture of the proposed Mars coaxial quadrotor, are introducing an alternative and more enhanced, from a control point of view concept, when compared in terms of autonomy to Ingenuity. Based on the presented design, the article will introduce the mathematical modelling and automatic control framework of the vehicle that will consist of a linearised model of a co-axial quadrotor and a corresponding Model Predictive Controller (MPC) for the trajectory tracking. Among the many models, proposed for the aerial flight on Mars, a reliable control architecture lacks in the related state of the art. The MPC based closed loop responses of the proposed MAV will be verified in different conditions during the flight with additional disturbances, induced to replicate a real flight scenario. In order to further validate the proposed control architecture and prove the efficacy of the suggested design, the introduced Mars coaxial quadrotor and the MPC scheme will be compared to a PID-type controller, similar to the Ingenuity helicopters control architecture for the position and the heading.
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We introduce the Control Toolbox (CT), an open-source C++ library for efficient modeling, control, estimation, trajectory optimization and Model Predictive Control. The CT is applicable to a broad class of dynamic systems but features interfaces to modeling tools specifically designed for robotic applications. This paper outlines the general concept of the toolbox, its main building blocks, and highlights selected application examples. The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems. The CT was designed for intuitive modeling of systems governed by ordinary differential or difference equations. It supports rapid prototyping of cost functions and constraints and provides standard interfaces for different optimal control solvers. To date, we support Single Shooting, the iterative Linear-Quadratic Regulator, Gauss-Newton Multiple Shooting and classical Direct Multiple Shooting. We provide interfaces to general purpose NLP solvers and Riccati-based linear-quadratic optimal control solvers. The CT was designed to solve large-scale optimal control and estimation problems efficiently and allows for online control of dynamic systems. Some of the key features to enable fast run-time performance are full compatibility with Automatic Differentiation, derivative code generation, and multi-threading. Still, the CT is designed as a modular framework whose building blocks can also be used for other control and estimation applications such as inverse dynamics control, extended Kalman filters or kinematic planning.
The ability to perform in-hand manipulation still remains an unsolved problem; having this capability would allow robots to perform sophisticated tasks requiring repositioning and reorienting of grasped objects. In this work, we present a novel non-anthropomorphic robot grasper with the ability to manipulate objects by means of active surfaces at the fingertips. Active surfaces are achieved by spherical rolling fingertips with two degrees of freedom (DoF) -- a pivoting motion for surface reorientation -- and a continuous rolling motion for moving the object. A further DoF is in the base of each finger, allowing the fingers to grasp objects over a range of size and shapes. Instantaneous kinematics was derived and objects were successfully manipulated both with a custom handcrafted control scheme as well as one learned through imitation learning, in simulation and experimentally on the hardware.
We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized approximation of the true continuous dynamics that can be integrated with model predictive control. Our approach is compatible with most Gaussian process approaches for system identification, and can learn an accurate model using modest amounts of training data. We validate our approach by learning the dynamics of an unstable system such as a segway with a 7-D state space and 2-D input space (using only one minute of data), and we show that the resulting controller is robust to unmodelled dynamics and disturbances, while state-of-the-art control methods based on nominal models can fail under small perturbations. Code is open sourced at https://github.com/learning-and-control/core .
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