Tag Archives: Dynamics

Abstraction of continuous control problems considered as MDPs

H. G. Tanner and A. Stager, Data-Driven Abstractions for Robots With Stochastic Dynamics, IEEE Transactions on Robotics, vol. 38, no. 3, pp. 1686-1702, June 2022 DOI: 10.1109/TRO.2021.3119209.

This article describes the construction of stochastic, data-based discrete abstractions for uncertain random processes continuous in time and space. Motivated by the fact that modeling processes often introduce errors which interfere with the implementation of control strategies, here the abstraction process proceeds in reverse: the methodology does not abstract models; rather it models abstractions. Specifically, it first formalizes a template for a family of stochastic abstractions, and then fits the parameters of that template to match the dynamics of the underlying process and ground the abstraction. The article also shows how the parameter-fitting approach can be implemented based on a probabilistic model validation approach which draws from randomized algorithms, and results in a discrete abstract model which is approximately simulated by the actual process physics, at a desired confidence level. In this way, the models afford the implementation of symbolic control plans with probabilistic guarantees at a desired level of fidelity.

A so-called universal approach for modelling and controlling robots

Tarokh, M., A unified kinematics modeling, optimization and control of universal robots: from serial and parallel manipulators to walking, rolling and hybrid robots, . Auton Robot 44, 1233–1248 (2020) DOI: 10.1007/s10514-020-09929-6.

The paper develops a unified kinematics modeling, optimization and control that is applicable to a wide range of autonomous and non-autonomous robots. These include hybrid robots that combine two or more modes of operations, such as combination of walking and rolling, or rolling and manipulation, as well as parallel robots in various configurations. The equations of motion are derived in compact forms that embed an optimization criterion. These equations are used to obtain various useful forms of the robot kinematics such as recursive, body and limb-end kinematic forms. Using the modeling, actuation and control equations are derived that ensure traversing a desired path while maintaining balanced operations and tip-over avoidance. Various simulation results are provided for a hybrid rolling-walking robot, which demonstrate the capabilities and effectiveness of the developed methodologies.

A new mathematical formulation of manipulator motion that simplifies dynamics and kinematics

Labbé, M. & Michaud, F., Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework, The International Journal of Robotics Research First Published May 20, 2018 DOI: 10.1177/0278364918772893.

This paper presents a novel unified theoretical framework for differential kinematics and dynamics for the optimization of complex robot motion. By introducing an 18×18 comprehensive motion transformation matrix, the forward differential kinematics and dynamics, including velocity and acceleration, can be written in a simple chain product similar to an ordinary rotational matrix. This formulation enables the analytical computation of derivatives of various physical quantities (e.g. link velocities, link accelerations, or joint torques) with respect to joint coordinates, velocities and accelerations for a robot trajectory in an efficient manner (O(NJ), where NJ is the number of the robot’s degree of freedom), which is useful for motion optimization. Practical implementation of gradient computation is demonstrated together with simulation results of robot motion optimization to validate the effectiveness of the proposed framework.