Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Controllability and motion planning of a multibody Chaplygin's sphere and Chaplygin's top

This paper studies local configuration controllability of multibody systems with nonholonomic constraints. As a nontrivial example of the theory, we consider the dynamics and control of a multibody spherical robot. Internal rotors and sliders are used as the mechanisms for control. Our model is based on equations developed by the second author for certain mechanical systems with nonholonomic constraints, e.g. Chaplygin's sphere and Chaplygin's top in particular, and the multibody framework for unconstrained mechanical systems developed by the first and third authors. Recent methods for determining controllability and path planning for multibody systems with symmetry are extended to treat a class of mechanical systems with nonholonomic constraints. Specificresults on the controllability and path planning of the spherical robot model are presented. Copyright © 2007 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58647/1/1259_ftp.pd

Space station attitude disturbance arising from internal motions

A source of space station attitude disturbances is identified. The attitude disturbance is driven by internal space station motions and is a direct result of conservation of angular momentum. Three examples are used to illustrate the effect: a planar three link system, a rigid carrier body with two moveable masses, and a nonplanar five link system. Simulation results are given to show the magnitude of the attitude change in each example. Factors which accentuate or attenuate this disturbance effect are discussed

Nonholonomic motion planning: steering using sinusoids

Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given

Control of autonomous multibody vehicles using artificial intelligence

The field of autonomous driving has been evolving rapidly within the last few years and a lot of research has been dedicated towards the control of autonomous vehicles, especially car-like ones. Due to the recent successes of artificial intelligence techniques, even more complex problems can be solved, such as the control of autonomous multibody vehicles. Multibody vehicles can accomplish transportation tasks in a faster and cheaper way compared to multiple individual mobile vehicles or robots. But even for a human, driving a truck-trailer is a challenging task. This is because of the complex structure of the vehicle and the maneuvers that it has to perform, such as reverse parking to a loading dock. In addition, the detailed technical solution for an autonomous truck is challenging and even though many single-domain solutions are available, e.g. for pathplanning, no holistic framework exists. Also, from the control point of view, designing such a controller is a high complexity problem, which makes it a widely used benchmark. In this thesis, a concept for a plurality of tasks is presented. In contrast to most of the existing literature, a holistic approach is developed which combines many stand-alone systems to one entire framework. The framework consists of a plurality of modules, such as modeling, pathplanning, training for neural networks, controlling, jack-knife avoidance, direction switching, simulation, visualization and testing. There are model-based and model-free control approaches and the system comprises various pathplanning methods and target types. It also accounts for noisy sensors and the simulation of whole environments. To achieve superior performance, several modules had to be developed, redesigned and interlinked with each other. A pathplanning module with multiple available methods optimizes the desired position by also providing an efficient implementation for trajectory following. Classical approaches, such as optimal control (LQR) and model predictive control (MPC) can safely control a truck with a given model. Machine learning based approaches, such as deep reinforcement learning, are designed, implemented, trained and tested successfully. Furthermore, the switching of the driving direction is enabled by continuous analysis of a cost function to avoid collisions and improve driving behavior. This thesis introduces a working system of all integrated modules. The system proposed can complete complex scenarios, including situations with buildings and partial trajectories. In thousands of simulations, the system using the LQR controller or the reinforcement learning agent had a success rate of >95 % in steering a truck with one trailer, even with added noise. For the development of autonomous vehicles, the implementation of AI at scale is important. This is why a digital twin of the truck-trailer is used to simulate the full system at a much higher speed than one can collect data in real life.Tesi

A motion planner for nonholonomic mobile robots

This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R^2 x S^1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentrate upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning