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

System Design, Motion Modelling and Planning for a Recon figurable Wheeled Mobile Robot

Over the past ve decades the use of mobile robotic rovers to perform in-situ scienti c investigations on the surfaces of the Moon and Mars has been tremendously in uential in shaping our understanding of these extraterrestrial environments. As robotic missions have evolved there has been a greater desire to explore more unstructured terrain. This has exposed mobility limitations with conventional rover designs such as getting stuck in soft soil or simply not being able to access rugged terrain. Increased mobility and terrain traversability are key requirements when considering designs for next generation planetary rovers. Coupled with these requirements is the need to autonomously navigate unstructured terrain by taking full advantage of increased mobility. To address these issues, a high degree-of-freedom recon gurable platform that is capable of energy intensive legged locomotion in obstacle-rich terrain as well as wheeled locomotion in benign terrain is proposed. The complexities of the planning task that considers the high degree-of-freedom state space of this platform are considerable. A variant of asymptotically optimal sampling-based planners that exploits the presence of dominant sub-spaces within a recon gurable mobile robot's kinematic structure is proposed to increase path quality and ensure platform safety. The contributions of this thesis include: the design and implementation of a highly mobile planetary analogue rover; motion modelling of the platform to enable novel locomotion modes, along with experimental validation of each of these capabilities; the sampling-based HBFMT* planner that hierarchically considers sub-spaces to better guide search of the complete state space; and experimental validation of the planner with the physical platform that demonstrates how the planner exploits the robot's capabilities to uidly transition between various physical geometric con gurations and wheeled/legged locomotion modes

A Planning Pipeline for Large Multi-Agent Missions

In complex multi-agent applications, human operators are often tasked with planning and managing large heterogeneous teams of humans and autonomous vehicles. Although the use of these autonomous vehicles broadens the scope of meaningful applications, many of their systems remain unintuitive and difficult to master for human operators whose expertise lies in the application domain and not at the platform level. Current research focuses on the development of individual capabilities necessary to plan multi-agent missions of this scope, placing little emphasis on the integration of these components in to a full pipeline. The work presented in this paper presents a complete and user-agnostic planning pipeline for large multiagent missions known as the HOLII GRAILLE. The system takes a holistic approach to mission planning by integrating capabilities in human machine interaction, flight path generation, and validation and verification. Components modules of the pipeline are explored on an individual level, as well as their integration into a whole system. Lastly, implications for future mission planning are discussed

The power dissipation method and kinematic reducibility of multiple-model robotic systems

This paper develops a formal connection between the power dissipation method (PDM) and Lagrangian mechanics, with specific application to robotic systems. Such a connection is necessary for understanding how some of the successes in motion planning and stabilization for smooth kinematic robotic systems can be extended to systems with frictional interactions and overconstrained systems. We establish this connection using the idea of a multiple-model system, and then show that multiple-model systems arise naturally in a number of instances, including those arising in cases traditionally addressed using the PDM. We then give necessary and sufficient conditions for a dynamic multiple-model system to be reducible to a kinematic multiple-model system. We use this result to show that solutions to the PDM are actually kinematic reductions of solutions to the Euler-Lagrange equations. We are particularly motivated by mechanical systems undergoing multiple intermittent frictional contacts, such as distributed manipulators, overconstrained wheeled vehicles, and objects that are manipulated by grasping or pushing. Examples illustrate how these results can provide insight into the analysis and control of physical systems

A system architecture for a planetary rover

Each planetary mission requires a complex space vehicle which integrates several functions to accomplish the mission and science objectives. A Mars Rover is one of these vehicles, and extends the normal spacecraft functionality with two additional functions: surface mobility and sample acquisition. All functions are assembled into a hierarchical and structured format to understand the complexities of interactions between functions during different mission times. It can graphically show data flow between functions, and most importantly, the necessary control flow to avoid unambiguous results. Diagrams are presented organizing the functions into a structured, block format where each block represents a major function at the system level. As such, there are six blocks representing telecomm, power, thermal, science, mobility and sampling under a supervisory block called Data Management/Executive. Each block is a simple collection of state machines arranged into a hierarchical order very close to the NASREM model for Telerobotics. Each layer within a block represents a level of control for a set of state machines that do the three primary interface functions: command, telemetry, and fault protection. This latter function is expanded to include automatic reactions to the environment as well as internal faults. Lastly, diagrams are presented that trace the system operations involved in moving from site to site after site selection. The diagrams clearly illustrate both the data and control flows. They also illustrate inter-block data transfers and a hierarchical approach to fault protection. This systems architecture can be used to determine functional requirements, interface specifications and be used as a mechanism for grouping subsystems (i.e., collecting groups of machines, or blocks consistent with good and testable implementations)