Toshiyuki Ohtsuka

Yuan Zhang, Shaohui Yang, Toshiyuki Ohtsuka et al.

Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a $\textbf{la}$tent $\textbf{l}$inear $\textbf{q}$uadratic $\textbf{r}$egulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.

Yuta Tanikawa, Yuga Tomita, Toshiyuki Ohtsuka

This study proposes a precipitation control framework integrating a realistic Numerical Weather Prediction (NWP) model with model predictive control (MPC). At each control instant in MPC, a finite-difference sensitivity matrix is constructed from the NWP model and used as a local linear model of how perturbations to the atmospheric state affect future precipitation. A sparse convex optimization problem is then solved to compute the control input, which is implemented as a perturbation to the atmospheric state. To reduce computational cost in sensitivity analysis, multiple grid points in the NWP model are treated collectively as a single block, and a uniform perturbation is applied to all points within each block. Moreover, a tailored convex optimization problem is introduced to effectively control the accumulated precipitation at the end of a weather event, using a prediction horizon much shorter than the entire event duration while promoting spatially sparse atmospheric perturbations. To evaluate the proposed MPC method, four control methods are compared: (i) initial-only open-loop optimal control (IO-OL), (ii) full-horizon open-loop optimal control (FH-OL), (iii) shrinking-horizon optimal control (SHOC) with a fixed terminal time, and (iv) single-move MPC with a fixed prediction-horizon length. Numerical experiments on a warm bubble benchmark demonstrate that MPC achieves precipitation reduction comparable to SHOC while reducing the total computational time relative to FH-OL and SHOC. Moreover, despite using a linear prediction model, MPC successfully achieves a challenging level of precipitation reduction, even when open-loop optimal control methods, namely, IO-OL and FH-OL, fail because of nonlinear atmospheric evolution. These findings suggest that MPC is a promising control framework for NWP-based precipitation reduction in complex weather events.

Sotaro Katayama, Toshiyuki Ohtsuka

This study proposes an efficient Newton-type method for the optimal control of switched systems under a given mode sequence. A mesh-refinement-based approach is utilized to discretize continuous-time optimal control problems (OCPs) and formulate a nonlinear program (NLP), which guarantees the local convergence of a Newton-type method. A dedicated structure-exploiting algorithm (Riccati recursion) is proposed to perform a Newton-type method for the NLP efficiently because its sparsity structure is different from a standard OCP. The proposed method computes each Newton step with linear time-complexity for the total number of discretization grids as the standard Riccati recursion algorithm. Additionally, the computation is always successful if the solution is sufficiently close to a local minimum. Conversely, general quadratic programming (QP) solvers cannot accomplish this because the Hessian matrix is inherently indefinite. Moreover, a modification on the reduced Hessian matrix is proposed using the nature of the Riccati recursion algorithm as the dynamic programming for a QP subproblem to enhance the convergence. A numerical comparison is conducted with off-the-shelf NLP solvers, which demonstrates that the proposed method is up to two orders of magnitude faster. Whole-body optimal control of quadrupedal gaits is also demonstrated and shows that the proposed method can achieve the whole-body model predictive control (MPC) of robotic systems with rigid contacts.

Sotaro Katayama, Toshiyuki Ohtsuka

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.

Sotaro Katayama, Toshiyuki Ohtsuka

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.

Sotaro Katayama, Toshiyuki Ohtsuka

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.