Sampling-based optimal kinodynamic planning with motion primitives

This paper proposes a novel sampling-based motion planner, which integrates in RRT* (Rapidly exploring Random Tree star) a database of pre-computed motion primitives to alleviate its computational load and allow for motion planning in a dynamic or partially known environment. The database is built by considering a set of initial and final state pairs in some grid space, and determining for each pair an optimal trajectory that is compatible with the system dynamics and constraints, while minimizing a cost. Nodes are progressively added to the tree {of feasible trajectories in the RRT* by extracting at random a sample in the gridded state space and selecting the best obstacle-free motion primitive in the database that joins it to an existing node. The tree is rewired if some nodes can be reached from the new sampled state through an obstacle-free motion primitive with lower cost. The computationally more intensive part of motion planning is thus moved to the preliminary offline phase of the database construction at the price of some performance degradation due to gridding. Grid resolution can be tuned so as to compromise between (sub)optimality and size of the database. The planner is shown to be asymptotically optimal as the grid resolution goes to zero and the number of sampled states grows to infinity

Graceful Navigation for Mobile Robots in Dynamic and Uncertain Environments.

The ability to navigate in everyday environments is a fundamental and necessary skill for any autonomous mobile agent that is intended to work with human users. The presence of pedestrians and other dynamic objects, however, makes the environment inherently dynamic and uncertain. To navigate in such environments, an agent must reason about the near future and make an optimal decision at each time step so that it can move safely toward the goal. Furthermore, for any application intended to carry passengers, it also must be able to move smoothly and comfortably, and the robot behavior needs to be customizable to match the preference of the individual users. Despite decades of progress in the field of motion planning and control, this remains a difficult challenge with existing methods. In this dissertation, we show that safe, comfortable, and customizable mobile robot navigation in dynamic and uncertain environments can be achieved via stochastic model predictive control. We view the problem of navigation in dynamic and uncertain environments as a continuous decision making process, where an agent with short-term predictive capability reasons about its situation and makes an informed decision at each time step. The problem of robot navigation in dynamic and uncertain environments is formulated as an on-line, finite-horizon policy and trajectory optimization problem under uncertainty. With our formulation, planning and control becomes fully integrated, which allows direct optimization of the performance measure. Furthermore, with our approach the problem becomes easy to solve, which allows our algorithm to run in real time on a single core of a typical laptop with off-the-shelf optimization packages. The work presented in this thesis extends the state-of-the-art in analytic control of mobile robots, sampling-based optimal path planning, and stochastic model predictive control. We believe that our work is a significant step toward safe and reliable autonomous navigation that is acceptable to human users.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120760/1/jongjinp_1.pd

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

Poli-RRT*: optimal RRT-based planning for constrained and feedback linearisable vehicle dynamics

This paper proposes a Rapidly exploring Random Trees planning strategy (Poli-RRT*) that computes optimal trajectories in presence of vehicle constraints (e.g., differential and actuation constraints) without approximating the nonlinear dynamics, but relying on exact linearisation. In this way, the optimal control problem that is introduced to determine the trajectories extending the tree can be expressed as a quadratic program and efficiently solved. Poli-RRT* is formulated and tested via simulation on a unicycle-like model of a vehicle subject to actuation constraints. Notably, the approach can be applied to any other feedback linearisable vehicle model, subject to different types of constraints

High-Dimensional Motion Planning and Learning Under Uncertain Conditions

Many existing path planning methods do not adequately account for uncertainty. Without uncertainty these existing techniques work well, but in real world environments they struggle due to inaccurate sensor models, arbitrarily moving obstacles, and uncertain action consequences. For example, picking up and storing childrens toys is a simple task for humans. Yet, for a robotic household robot the task can be daunting. The room must be modeled with sensors, which may or may not detect all the strewn toys. The robot must be able to detect and avoid the child who may be moving the very toys that the robot is tasked with cleaning. Finally, if the robot missteps and places a foot on a toy, it must be able to compensate for the unexpected consequences of its actions. This example demonstrates that even simple human tasks are fraught with uncertainties that must be accounted for in robotic path planning algorithms. This work presents the first steps towards migrating sampling-based path planning methods to real world environments by addressing three different types of uncertainty: (1) model uncertainty, (2) spatio-temporal obstacle uncertainty (moving obstacles) and (3) action consequence uncertainty. Uncertainty is encoded directly into path planning through a data structure in order to successfully and efficiently identify safe robot paths in sensed environments with noise. This encoding produces comparable clearance paths to other planning methods which are a known for high clearance, but at an order of magnitude less computational cost. It also shows that formal control theory methods combined with path planning provides a technique that has a 95% collision-free navigation rate with 300 moving obstacles. Finally, it demonstrates that reinforcement learning can be combined with planning data structures to autonomously learn motion controls of a seven degree of freedom robot despite a low computational cost despite the number of dimensions