Optimisation-based verification process of obstacle avoidance systems for unmanned vehicles

This thesis deals with safety verification analysis of collision avoidance systems for unmanned vehicles. The safety of the vehicle is dependent on collision avoidance algorithms and associated control laws, and it must be proven that the collision avoidance algorithms and controllers are functioning correctly in all nominal conditions, various failure conditions and in the presence of possible variations in the vehicle and operational environment. The current widely used exhaustive search based approaches are not suitable for safety analysis of autonomous vehicles due to the large number of possible variations and the complexity of algorithms and the systems. To address this topic, a new optimisation-based verification method is developed to verify the safety of collision avoidance systems. The proposed verification method formulates the worst case analysis problem arising the verification of collision avoidance systems into an optimisation problem and employs optimisation algorithms to automatically search the worst cases. Minimum distance to the obstacle during the collision avoidance manoeuvre is defined as the objective function of the optimisation problem, and realistic simulation consisting of the detailed vehicle dynamics, the operational environment, the collision avoidance algorithm and low level control laws is embedded in the optimisation process. This enables the verification process to take into account the parameters variations in the vehicle, the change of the environment, the uncertainties in sensors, and in particular the mismatching between model used for developing the collision avoidance algorithms and the real vehicle. It is shown that the resultant simulation based optimisation problem is non-convex and there might be many local optima. To illustrate and investigate the proposed optimisation based verification process, the potential field method and decision making collision avoidance method are chosen as an obstacle avoidance candidate technique for verification study. Five benchmark case studies are investigated in this thesis: static obstacle avoidance system of a simple unicycle robot, moving obstacle avoidance system for a Pioneer 3DX robot, and a 6 Degrees of Freedom fixed wing Unmanned Aerial Vehicle with static and moving collision avoidance algorithms. It is proven that although a local optimisation method for nonlinear optimisation is quite efficient, it is not able to find the most dangerous situation. Results in this thesis show that, among all the global optimisation methods that have been investigated, the DIviding RECTangle method provides most promising performance for verification of collision avoidance functions in terms of guaranteed capability in searching worst scenarios

A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles

We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass. We present a Hamilton-Jacobi formulation of the problem that resolves time-optimal paths and considers the geometry of the vehicle

Motion Planning and Posture Control of Multiple n-link Doubly Nonholonomic Manipulators

The paper considers the problem of motion planning and posture control of multiple n-link doubly nonholonomic mobile manipulators in an obstacle-cluttered and bounded workspace. The workspace is constrained with the existence of an arbitrary number of fixed obstacles (disks, rods and curves), artificial obstacles and moving obstacles. The coordination of multiple n-link doubly nonholonomic mobile manipulators subjected to such constraints becomes therefore a challenging navigational and steering problem that few papers have considered in the past. Our approach to developing the controllers, which are novel decentralized nonlinear acceleration controllers, is based on a Lyapunov control scheme that is not only intuitively understandable but also allows simple but rigorous development of the controllers. Via the scheme, we showed that the avoidance of all types of obstacles was possible, that the manipulators could reach a neighborhood of their goal and that their final orientation approximated the desired orientation. Computer simulations illustrate these results. KEYWORDS: Lyapunov-based control scheme; Doubly nonholonomic manipulators; Ghost parking bays; Minimum distance technique; Stability; Kinodynamic constraints

A Discrete Geometric Optimal Control Framework for Systems with Symmetries

This paper studies the optimal motion control of mechanical systems through a discrete geometric approach. At the core of our formulation is a discrete Lagrange-d’Alembert- Pontryagin variational principle, from which are derived discrete equations of motion that serve as constraints in our optimization framework. We apply this discrete mechanical approach to holonomic systems with symmetries and, as a result, geometric structure and motion invariants are preserved. We illustrate our method by computing optimal trajectories for a simple model of an air vehicle flying through a digital terrain elevation map, and point out some of the numerical benefits that ensue

A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima

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

Optimisation-based verification process of obstacle avoidance systems for unicycle-like mobile robots

This paper presents an optimisation-based verification process for obstacle avoidance systems of a unicycle-like mobile robot. It is a novel approach for the collision avoidance verification process. Local and global optimisation based verification processes are developed to find the worst-case parameters and the worst-case distance between the robot and an obstacle. The kinematic and dynamic model of the unicycle-like mobile robot is first introduced with force and torque as the inputs. The design of the control system is split into two parts. One is velocity and rotation using the robot dynamics, and the other is the incremental motion planning for robot kinematics. The artificial potential field method is chosen as a path planning and obstacle avoidance candidate technique for verification study as it is simple and widely used. Different optimisation algorithms are applied and compared for the purpose of verification. It is shown that even for a simple case study where only mass and inertia variations are considered, a local optimization based verification method may fail to identify the worst case. Two global optimisation methods have been investigated: genetic algorithms (GAs) and GLOBAL algorithms. Both of these methods successfully find the worst case. The verification process confirms that the obstacle avoidance algorithm functions correctly in the presence of all the possible parameter variations