接触を伴うロボットの高速なモデル予測制御

京都大学新制・課程博士博士(情報学)甲第24266号情博第810号京都大学大学院情報学研究科システム科学専攻(主査)教授 大塚 敏之, 教授 石井 信, 教授 森本 淳学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA

Efficient Riccati recursion for optimal control problems with pure-state equality constraints

A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed state-control constraint such that the constraint is expressed by variables at a certain previous time stage. It is showed that if the solution satisfies the second-order sufficient conditions of the OCP with the transformed mixed state-control constraints, it is a local minimum of the OCP with the original pure-state constraints. A Riccati recursion algorithm is derived to solve the OCP using the transformed constraints with linear time complexity in the grid number of the horizon, in contrast to a previous approach that scales cubically with respect to the total dimension of the pure-state equality constraints. Numerical experiments on the whole-body optimal control of quadrupedal gaits that involve pure-state equality constraints owing to contact switches demonstrate the effectiveness of the proposed method over existing approaches.Comment: 8 pages, 3 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Inverse dynamics‐based formulation of finite horizon optimal control problems for rigid‐body systems

We propose a formulation of the finite horizon optimal control problem (FHOCP) based on inverse dynamics for general open-chain rigid-body systems, which reduces the computational cost from the conventional formulation based on forward dynamics. We regard the generalized acceleration as a decision variable and inverse dynamics as an equality constraint. To treat under-actuated systems with inverse dynamics that are well defined only to fully actuated systems, that is, to consider passive joints in this FHOCP, we add an equality constraint to zero the corresponding generalized torques. We include the contact forces in the decision variables of this FHOCP and treat the contact constraints using Baumgarte's stabilization method for numerical stability. We derive the optimality conditions and formulate the two-point boundary-value problem that can be efficiently solved using the recursive Newton–Euler algorithm (RNEA) and the partial derivatives of RNEA. We conducted three numerical experiments on model predictive control based on the proposed formulation to demonstrate its effectiveness. The first experiment involved simulating a swing-up control of a four-link arm with a passive joint and showed that the proposed formulation is effective for under-actuated systems. The second one involved comparing the proposed formulation with the conventional forward-dynamics-based formulation with various numbers of joints and showed that the proposed formulation reduces computational cost regardless of the number of joints. The third experiment involved simulating a whole-body control of a quadruped robot, a floating-base system having four contacts with the ground, and showed that the proposed formulation is applicable even for floating-base systems with contacts

A moving switching sequence approach for nonlinear model predictive control of switched systems with state‐dependent switches and state jumps

不連続な変化を伴う実時間最適制御の高速アルゴリズムの開発に成功 --2足歩行ロボットなどの限界性能を引き出す手法--. 京都大学プレスリリース. 2019-11-12.In this paper, we propose an approach for real‐time implementation of nonlinear model predictive control (NMPC) for switched systems with state‐dependent switches called the moving switching sequence approach. In this approach, the switching sequence on the horizon moves to the present time at each time as well as the optimal state trajectory and the optimal control input on the horizon. We assume that the switching sequence is basically invariant until the first predicted switching time reaches the current time or a new switch enters the horizon. This assumption is reasonable in NMPC for systems with state‐dependent switches and reduces computational cost significantly compared with the direct optimization of the switching sequence all over the horizon. We update the switching sequence by checking whether an additional switch occurs or not at the last interval of the present switching sequence and whether the actual switch occurs or not between the current time and the next sampling time. We propose an algorithm consisting of two parts: (1) the local optimization of the control input and switching instants by solving the two‐point boundary‐value problem for the whole horizon under a given switching sequence and (2) the detection of an additional switch and the reconstruction of the solution taking into account the additional switch. We demonstrate the effectiveness of the proposed method through numerical simulations of a compass‐like biped walking robot, which contains state‐dependent switches and state jumps

Efficient solution method based on inverse dynamics for optimal control problems of rigid body systems

We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques, as optimization variables and treat the inverse dynamics as an equality constraint. We eliminate the update of the control input torques from the linear equation of Newton's method by applying condensing for inverse dynamics. The size of the resultant linear equation is the same as that of the multiple-shooting method based on forward dynamics except for the variables related to the passive joints and contacts. Compared with the conventional methods based on forward dynamics, the proposed method reduces the computational cost of the dynamics and their sensitivities by utilizing the recursive Newton-Euler algorithm (RNEA) and its partial derivatives. In addition, it increases the sparsity of the Hessian of the Karush-Kuhn-Tucker conditions, which reduces the computational cost, e.g., of Riccati recursion. Numerical experiments show that the proposed method outperforms state-of-the-art implementations of differential dynamic programming based on forward dynamics in terms of computational time and numerical robustness.Comment: 7 pages, 3 figures. This paper has been accepted to be presented 2021 IEEE International Conference on Robotics and Automation (ICRA2021

Lifted contact dynamics for efficient optimal control of rigid body systems with contacts

We propose a novel and efficient lifting approach for the optimal control of rigid-body systems with contacts to improve the convergence properties of Newton-type methods. To relax the high nonlinearity, we consider the state, acceleration, contact forces, and control input torques, as optimization variables and the inverse dynamics and acceleration constraints on the contact frames as equality constraints. We eliminate the update of the acceleration, contact forces, and their dual variables from the linear equation to be solved in each Newton-type iteration in an efficient manner. As a result, the computational cost per Newton-type iteration is almost identical to that of the conventional non-lifted Newton-type iteration that embeds contact dynamics in the state equation. We conducted numerical experiments on the whole-body optimal control of various quadrupedal gaits subject to the friction cone constraints considered in interior-point methods and demonstrated that the proposed method can significantly increase the convergence speed to more than twice that of the conventional non-lifted approach.Comment: 8 pages, 4 figures. This work has been accepted to be presented at the 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2022

Whole-body model predictive control with rigid contacts via online switching time optimization

This study presents a whole-body model predictive control (MPC) of robotic systems with rigid contacts, under a given contact sequence using online switching time optimization (STO). We treat robot dynamics with rigid contacts as a switched system and formulate an optimal control problem of switched systems to implement the MPC. We utilize an efficient solution algorithm for the MPC problem that optimizes the switching times and trajectory simultaneously. The present efficient algorithm, unlike inefficient existing methods, enables online optimization as well as switching times. The proposed MPC with online STO is compared over the conventional MPC with fixed switching times, through numerical simulations of dynamic jumping motions of a quadruped robot. In the simulation comparison, the proposed MPC successfully controls the dynamic jumping motions in twice as many cases as the conventional MPC, which indicates that the proposed method extends the ability of the whole-body MPC. We further conduct hardware experiments on the quadrupedal robot Unitree A1 and prove that the proposed method achieves dynamic motions on the real robot.Comment: 8 pages, 10 figures. This work has been accepted to be presented at the 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2022