Sotaro Katayama

Model predictive control (MPC) of legged and humanoid robotic systems has been an active research topic in the past decade. While MPC for robotic systems has a long history, its paradigm such as problem formulations and algorithms has changed along with the recent drastic progress in robot hardware, computational processors, and algorithms. This survey paper reviews recent progress on MPC for legged and humanoid robotics from the following three points of view. First, we review a variety of dyna

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

We present an automatic code generation tool, AutoGenU for Jupyter, for nonlinear model predictive control (NMPC) with a user-friendly and interactive interface utilizing JupyterLab and Jupyter Notebook. We utilize a symbolic computation package SymPy for automatic C++ code generation. We also developed numerical solvers of NMPC using the continuation/GMRES (C/GMRES) method and multiple-shooting-based C/GMRES method in C++. AutoGenU for Jupyter provides the simulation environment of NMPC with th

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 e

We propose an efficient solution method of finite horizon optimal control problems (FHOCPs) for fixed-based rigid-body systems based on inverse dynamics. Our method can reduce the computational cost compared with the conventional FHOCP based on forward dynamics. We reformulate the FHOCP for the rigid-body systems by utilizing the generalized acceleration as the decision variables and inverse dynamics as the equality constraint. We derive the necessary conditions of the optimal control, namely, t

In this work, we propose a real-time algorithm of nonlinear model predictive control (NMPC) for a class of switched systems with state-dependent switches and state jumps based on the continuation/GMRES (C/GMRES) method. This approach utilizes the characteristic of NMPC that the optimal solution changes continuously with respect to time and optimizes control input and switching instants simultaneously by updating them at each sampling time. To avoid difficulty in updating the solution based on th

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 i

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 fro

This paper presents a nonlinear model predictive control (NMPC) toward versatile motion generation for the telescopic-wheeled-legged robot Tachyon 3, the unique hardware structure of which poses challenges in control and motion planning. We apply the full-centroidal NMPC formulation with dedicated constraints that can capture the accurate kinematics and dynamics of Tachyon 3. We have developed a control pipeline that includes an internal state integrator to apply NMPC to Tachyon 3, the actuators

We propose an efficient algorithm for the optimal control problems (OCPs) of nonlinear switched systems that optimizes the control input and switching instants simultaneously for a given switching sequence. We consider the switching instants as the optimization variables and formulate the OCP based on the direct multiple shooting method. We derive a linear equation to be solved in Newton’s method and propose a Riccati recursion algorithm to solve the linear equation efficiently. The computationa

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 loc

In this work, we present nonlinear model predictive control for switched systems with externally forced switchings, in which a continuous control input and binary switching signal are optimized simultaneously. We introduce a scenario tree that represents the combination of active subsystems on the predictive horizon. We propose a computation strategy using the continuous characteristic of a solution to the optimal control problem for each scenario. We present a numerical experiment of an applica

In this paper, we propose a real-time algorithm of nonlinear model predictive control for systems with state jumps based on the C/GMRES method. Applying a standard numerical solution method directly to an optimal control problem with state jumps is generally difficult because of additional constraints associated with the state jumps. We introduce a penalty function method to avoid these difficulties. We demonstrate the effectiveness of the proposed method using a numerical simulation of a compas

This paper presents a stochastic/robust nonlinear model predictive control (NMPC) to enhance the robustness of model-based legged locomotion against contact uncertainties. We integrate the contact uncertainties into the covariance propagation of stochastic/robust NMPC framework by lever-aging the guard saltation matrix and an extended Kalman filter-like covariance update. We achieve fast stochastic/robust NMPC computation by utilizing the zero-order algorithm with additional improvements in comp

Sim-to-real reinforcement learning (RL) for humanoid robots with high-gear ratio actuators remains challenging due to complex actuator dynamics and the absence of torque sensors. To address this, we propose a novel RL framework leveraging foot-mounted inertial measurement units (IMUs). Instead of pursuing detailed actuator modeling and system identification, we utilize foot-mounted IMU measurements to enhance rapid stabilization capabilities over challenging terrains. Additionally, we propose sy