Deterministic Kinodynamic Planning with hardware demonstrations

Abstract

DKP (Deterministic Kinodynamic Planning) is a bottom-up trajectory planner for robots with flatnessproperties. DKP builds an exploration tree of which the branches are spline trajectories. DKP employs an A * -like algorithm to select which branch of the tree to grow. The selected trajectories are then grown in a propagation process which respects the kinematic constraints, such as linear/angular speed limits or obstacle avoidance. In addition, DKP produces trajectories that are immediately executable by the robot. Various experiments are provided to show the ability of DKP to effectively handle complex environments with one or more robots. I. INTRODUCTIONComputing a trajectory that takes into account both kinematic and dynamic constraints is known as kinodynamic planning [5], and is proven to be PSPACE-hard [22].Decoupled approaches separate kinodynamic planning in two successive problems; first, compute a path taking into account a part of the problem constraints (classically obstacles) and, then, smooth this path with the remaining constraints to make the solution admissible by the robot. The efficiency of decoupled approaches, such as variants of Elastic Bands [23], is explained by the fact that they are generally customized for specific kinodynamic problems [15]. They also provide bounds on the computation time, allowing on-line planning, which explains their wide usage. However, decoupled approaches present difficulties to solve complicated problems, with many degrees of freedom. Moreover, they suffer from incompleteness issues: since the initial path is not guaranteed to be feasible by the robot, the path smoothing phase may fail to satisfy all kinodynamic constraints or fail to find a solution even if one exists.To solve these difficulties [18], we can distinguish two categories of hybrid approaches which incorporate a local motion planner (selection process) within a global path planner (propagation process) to ensure the respect of constraints. The first category contains heavily customized approaches: both local and global motion planner are then designed to generate complex local maneuvers [11] and/or improve the quality of the global path to be tracked. They successfully deal with very specific problems, such as [6] which integrates perception sensors in the local planner; or the multi resolution approaches like AD * [18].

Collision Avoidance from Multiple Passive Agents with Partially Predictable Behavior

“…Figure 6 shows the same for the double integrator. (5,10), for selected β, while avoiding collision with a static passive agent at (12,9). The control parameter η was set to 3.…”

“…In [12,13], the problem of kinodynamic motion planning for a robot in a dynamic environment was addressed. The proposed approaches explore the state-time space of the robot to find a collision free path to the goal, while it was assumed that the entire path of the passive agents is known.…”

Towards Cognitive Steering Behaviours for Two-Wheeled Robots

“…As shown in (Gaillard et al, 2011), DKP can deal with this kind of overtaking situation. From our point of view, the solution (the one from DKP used alone or solutions from other hybrid trajectory planners) is a "forward obstacle avoidance": there is no reasoning or adaptation about the kinematic constraints or the samples duration during the trajectory planning (except for the backtracking process).…”

“…The trajectory tree contains trajectory samples dynamically extended using the steering parameters from the steering behaviours expressed in the steering tree. We use our sample-based approach named DKP, first presented in (Gaillard et al, 2010) and successfully applied on real robots (Gaillard et al, 2011). With its selection/propagation architecture, DKP provides properties for the low layer that we need to build a cognitive trajectory planner.…”