Motion Planning for Mobile Robots Via Sampling-Based Model Predictive Optimization

Abstract

Path planning is a method that determines a path, consecutive states, between a start state and goal state, LaValle (2006). However, in motion planning that path must be parameterized by time to create a trajectory. Consequently, not only is the path determined, but the time the vehicle moves along the path. To be successful at motion planning, a vehicle model must be incorporated into the trajectory computation. The motivation in utilizing a vehicle model is to provide the opportunity to predict the vehicle’s motion resulting from a variety of system inputs. The kinematic model enforces the vehicle kinematic constraints (i.e. turn radius, etc.), on the vehicle that limit the output space (state space). However, the kinematic model is limited because it does not take into account the forces acting on the vehicle. The dynamic model incorporates more useful information about the vehicle’s motion than the kinematic model. It describes the feasible control inputs, velocities, acceleration and vehicle/terrain interaction phenomena. Motion planning that will require the vehicle to perform close to its limits (i.e. extreme terrains, frequent acceleration, etc.) will need the dynamic model. Examples of missions that would benefit from using a dynamic model in the planning are time optimal motion planning, energy efficient motion planning and planning in the presence of faults, Yu et al. (2010). Sampling-based methods represent a type of model based motion planning algorithm. These methods incorporate the system model. There are current sampling-based planners that should be discussed: The Rapidly-Exploring Random Tree (RRT) Planner, Randomized A (RA) algorithm, and the Synergistic Combination of Layers of Planning (SyCLoP) multi-layered planning framework. The Rapidly-Exploring Random Tree Planner was one of the first single-query sampling based planners and serves as a foundation upon which many current algorithms are developed. The RRT Planner is very efficient and has been used in many applications including manipulator path planning, Kuffner & LaValle. (2000), and robot trajectory planning, LaValle & Kuffner (2001). However, the RRT Planner has the major drawback of lacking any sort of optimization other than a bias towards exploring the search space. The RA algorithm, which was designed based on the RRT Planner, addresses this drawback by combining the RRT Planner with an A algorithm. The SyCLoP framework is 11