Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping

Wheeled Mobile Robots: State of the Art Overview and Kinematic Comparison Among Three Omnidirectional Locomotion Strategies

In the last decades, mobile robotics has become a very interesting research topic in the feld of robotics, mainly because of population ageing and the recent pandemic emergency caused by Covid-19. Against this context, the paper presents an overview on wheeled mobile robot (WMR), which have a central role in nowadays scenario. In particular, the paper describes the most commonly adopted locomotion strategies, perception systems, control architectures and navigation approaches. After having analyzed the state of the art, this paper focuses on the kinematics of three omnidirectional platforms: a four mecanum wheels robot (4WD), a three omni wheel platform (3WD) and a two swerve-drive system (2SWD). Through a dimensionless approach, these three platforms are compared to understand how their mobility is afected by the wheel speed limitations that are present in every practical application. This original comparison has not been already presented by the literature and it can be used to improve our understanding of the kinematics of these mobile robots and to guide the selection of the most appropriate locomotion system according to the specifc application

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

Axel: A Minimalist Tethered Rover for Exploration of Extreme Planetary Terrains

Recent scientific findings suggest that some of the most interesting sites for future exploration of planetary surfaces lie in terrains that are currently inaccessible to conventional robotic rovers. To provide robust and flexible access to these terrains, we have been developing Axel, the robotic rover. Axel is a lightweight two-wheeled vehicle that can access steep terrains and negotiate relatively large obstacles because of its actively managed tether and novel wheel design. This article reviews the Axel system and focuses on those system components that affect Axel's steep terrain mobility. Experimental demonstrations of Axel on sloped and rocky terrains are presented