Nonholonomic Motion Planning Strategy for Underactuated Manipulator

This paper develops nonholonomic motion planning strategy for three-joint underactuated manipulator, which uses only two actuators and can be converted into chained form. Since the manipulator was designed focusing on the control simplicity, there are several issues for motion planning, mainly including transformation singularity, path estimation, and trajectory robustness in the presence of initial errors, which need to be considered. Although many existing motion planning control laws for chained form system can be directly applied to the manipulator and steer it to desired configuration, coordinate transformation singularities often happen. We propose two mathematical techniques to avoid the transformation singularities. Then, two evaluation indicators are defined and used to estimate control precision and linear approximation capability. In the end, the initial error sensitivity matrix is introduced to describe the interference sensitivity, which is called robustness. The simulation and experimental results show that an efficient and robust resultant path of three-joint underactuated manipulator can be successfully obtained by use of the motion planning strategy we presented

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

A Geometric Approach to Trajectory Planning for Underactuated Mechanical Systems

In the last decade, multi-rotors flying robots had a rapid development in industry and hobbyist communities thanks to the affordable cost and their availability of parts and components. The high number of degrees of freedom and the challenging dynamics of multi-rotors gave rise to new research problems. In particular, we are interested in the development of technologies for an autonomous fly that would al- low using multi-rotors systems to be used in contexts where the presence of humans is denied, for example in post-disaster areas or during search-and-rescue operations. Multi-rotors are an example of a larger category of robots, called \u201cunder-actuated mechanical systems\u201d (UMS) where the number of actuated degrees of freedom (DoF) is less than the number of available DoF. This thesis applies methods com- ing from geometric mechanics to study the under-actuation problem and proposes a novel method, based on the Hamiltonian formalism, to plan a feasible trajectory for UMS. We first show the application of a method called \u201cVariational Constrained System approach\u201d to a cart-pole example. We discovered that it is not possible to extend this method to generic UMS because it is valid only for a sub-class of UMS, called \u201csuper-articulated\u201d mechanical system. To overcome this limitation, we wrote the Hamilton equations of the quad- rotor and we apply a numerical \u201cdi- rect method\u201d to compute a feasible trajectory that satisfies system and endpoint constraints. We found that by including the system energy in the multi-rotor states, we are able to compute maneuvers that cannot be planned with other methods and that overcome the under-actuation constraints. To demonstrate the benefit of the method developed, we built a custom quad- rotor and an experimental setup with different obstacles, such as a gap in a wall and we show the correctness of the trajectory computed with the new method

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

Perception Based Navigation for Underactuated Robots.

Robot autonomous navigation is a very active field of robotics. In this thesis we propose a hierarchical approach to a class of underactuated robots by composing a collection of local controllers with well understood domains of attraction. We start by addressing the problem of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal. We summarize with simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons. Next we explore the possibility of adapting the resulting first order hybrid feedback controller to its dynamical counterpart by introducing tunable damping terms in the control law. Just as gradient controllers for standard quasi-static mechanical systems give rise to generalized "PD-style" controllers for dynamical versions of those standard systems, we show that it is possible to construct similar "lifts" in the presence of non-holonomic constraints notwithstanding the necessary absence of point attractors. Simulation results corroborate the proposed lift. Finally we present an implementation of a fully autonomous navigation application for a legged robot. The robot adapts its leg trajectory parameters by recourse to a discrete gradient descent algorithm, while managing its experiments and outcome measurements autonomously via the navigation visual servoing algorithms proposed in this thesis.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58412/1/glopes_1.pd

Sampled-Data Control of Invariant Systems on Exponential Lie Groups

This thesis examines the dynamics and control of a class of systems furnished by kinematic systems on exponential matrix Lie groups, when the plant evolves in continuous-time, but whose controller is implemented in discrete-time. This setup is called sampled-data and is ubiquitous in applied control. The class of Lie groups under consideration is motivated by our previous work concerning a similar class of kinematic systems on commutative Lie groups, whose local dynamics were found to be linear, which greatly facilitated control design. This raised the natural question of what class of systems on Lie groups, or class of Lie groups, would admit global characterizations of stability based on the linear part of their local dynamics. As we show in this thesis, the answer is---or at least includes---left- or right-invariant systems on exponential Lie groups, which are necessarily solvable, nilpotent, or commutative. We examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference equation has three key properties that facilitate our analysis: 1) its Lie series expansion enjoys a type of strong convergence; 2) the origin is an equilibrium; 3) the algebraic ideals enumerated in the lower central series of the Lie algebra are dynamically invariant. We show that certain global stability properties are implied by stability of the Jacobian linearization of dynamics at the origin, in particular, global asymptotic stability. If the Lie algebra is nilpotent, then the origin enjoys semiglobal exponential stability. We then study the synchronization of networks of identical continuous-time kinematic agents on a matrix Lie group, controlled by discrete-time controllers with constant sampling periods and directed, weighted communication graphs with a globally reachable node. We present a smooth, distributed, nonlinear discrete-time control law that achieves global synchronization on exponential matrix Lie groups, which include simply connected nilpotent Lie groups as a special case. Synchronization is generally asymptotic, but if the Lie group is nilpotent, then synchronization is achieved at an exponential rate. We first linearize the synchronization error dynamics at the identity, and show that the proposed controller achieves local exponential synchronization on any Lie group. Building on the local analysis, we show that, if the Lie group is exponential, then synchronization is global. We provide conditions for deadbeat convergence when the communication graph is unweighted and complete. Lastly, we examine a regulator problem for a class of fully actuated continuous-time kinematic systems on Lie groups, using a discrete-time controller with constant sampling period. We present a smooth discrete-time control law that achieves global regulation on simply connected nilpotent Lie groups. We first solve the problem when both the plant state and exosystem state are available for feedback. We then present a control law for the case where the plant state and a so-called plant output are available for feedback. The class of plant outputs considered includes, for example, the quantity to be regulated. This class of output allows us to use the classical Luenberger observer to estimate the exosystem states. In the full-information case, the regulation quantity on the Lie algebra is shown to decay exponentially to zero, which implies that it tends asymptotically to the identity on the Lie group

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

Underwater Robots Part II: Existing Solutions and Open Issues

National audienceThis paper constitutes the second part of a general overview of underwater robotics. The first part is titled: Underwater Robots Part I: current systems and problem pose. The works referenced as (Name*, year) have been already cited on the first part of the paper, and the details of these references can be found in the section 7 of the paper titled Underwater Robots Part I: current systems and problem pose. The mathematical notation used in this paper is defined in section 4 of the paper Underwater Robots Part I: current systems and problem pose

Robust hybrid control for autonomous vehicle motion planning

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2001.Includes bibliographical references (p. 141-150).This dissertation focuses on the problem of motion planning for agile autonomous vehicles. In realistic situations, the motion planning problem must be solved in real-time, in a dynamic and uncertain environment. The fulfillment of the mission objectives might also require the exploitation of the full maneuvering capabilities of the vehicle. The main contribution of the dissertation is the development of a new computational and modelling framework (the Maneuver Automaton), and related algorithms, for steering underactuated, nonholonomic mechanical systems. The proposed approach is based on a quantization of the system's dynamics, by which the feasible nominal system trajectories are restricted to the family of curves that can be obtained by the interconnection of suitably defined primitives. This can be seen as a formalization of the concept of "maneuver", allowing for the construction of a framework amenable to mathematical programming. This motion planning framework is applicable to all time-invariant dynamical systems which admit dynamic symmetries and relative equilibria. No other assumptions are made on the dynamics, thus resulting in exact motion planning techniques of general applicability. Building on a relatively expensive off-line computation phase, we provide algorithms viable for real-time applications. A fundamental advantage of this approach is the ability to provide a mathematical foundation for generating a provably stable and consistent hierarchical system, and for developing the tools to analyze the robustness of the system in the presence of uncertainty and/or disturbances.(cont.) In the second part of the dissertation, a randomized algorithm is proposed for real-time motion planning in a dynamic environment. By employing the optimal control solution in a free space developed for the maneuver automaton (or for any other general system), we present a motion planning algorithm with probabilistic convergence and performance guarantees, and hard safety guarantees, even in the face of finite computation times. The proposed methodologies are applicable to a very large class of autonomous vehicles: throughout the dissertation, examples, simulation and experimental results are presented and discussed, involving a variety of mechanical systems, ranging from simple academic examples and laboratory setups, to detailed models of small autonomous helicopters.by Emilio Frazzoli.Ph.D