Physics-based motion planning is a challenging task, since it requires the computation of the robot motions while allowing possible interactions with (some of) the obstacles in the environment. Kinodynamic motion planners equipped with a dynamic engine acting as state propagator are usually used for that purpose. The difficulties arise in the setting of the adequate forces for the interactions and because these interactions may change the pose of the manipulatable obstacles, thus either facilitating or preventing the finding of a solution path. The use of knowledge can alleviate the stated difficulties. This paper proposes the use of an enhanced state propagator composed of a dynamic engine and a low-level geometric reasoning process that is used to determine how to interact with the objects, i.e. from where and with which forces. The proposal, called κ-PMP can be used with any kinodynamic planner, thus giving rise to e.g. κ-RRT. The approach also includes a preprocessing step that infers from a semantic abstract knowledge described in terms of an ontology the manipulation knowledge required by the reasoning process. The proposed approach has been validated with several examples involving an holonomic mobile robot, a robot with differential constraints and a serial manipulator, and benchmarked using several state-of-the art kinodynamic planners. The results showed a significant difference in the power consumption with respect to simple physics-based planning, an improvement in the success rate and in the quality of the solution paths.
In all the above stated planners the control sampling range is usually set at the start and remains the same in the entire planning process; on each state the controls are randomly sampled from the given control range that results in the robot motion. Beside sampling-based algorithms there are some other recently proposed approaches for kinodynamic motion planning, such as the Covariant Hamiltonian Optimization for Motion Planning (CHOMP @cite_23 ). These approaches mainly focus on the optimization (such as smoothness) but can be used as stand alone motion planners for computing collision-free trajectories.
@cite_23
2054585537 2024382047 2142298978 1485487406
We present Kinodynamic RRT*, an incremental sampling-based approach for asymptotically optimal motion planning for robots with linear dynamics. Our approach extends RRT*, which was introduced for holonomic robots [10], by using a fixed-final-state-free-final-time controller that optimally connects any pair of states, where the cost function is expressed as a trade-off between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on RRT* for kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closed-form solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT* at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4-D state space and double integrator dynamics, (ii) an aerial vehicle with a 10-D state space and linearized quadrotor dynamics, and (iii) a car-like robot with a 5-D state space and non-linear dynamics. As sampling-based motion planners become faster, they can be reexecuted more frequently by a robot during task execution to react to uncertainty in robot motion, obstacle motion, sensing noise, and uncertainty in the robot's kinematic model. We investigate and analyze high-frequency replanning (HFR) where, during each period, fast sampling-based motion planners are executed in parallel as the robot simultaneously executes the first action of the best motion plan from the previous period. We consider discrete-time systems with stochastic nonlinear (but linearizable) dynamics and observation models with noise drawn from zero mean Gaussian distributions. The objective is to maximize the probability of success (i.e., avoid collision with obstacles and reach the goal) or to minimize path length subject to a lower bound on the probability of success. We show that, as parallel computation power increases, HFR offers asymptotic optimality for these objectives during each period for goal-oriented problems. We then demonstrate the effectiveness of HFR for holonomic and nonholonomic robots including car-like vehicles and steerable medical needles. This paper presents a type of motion primitives that can be used for building efficient kinodynamic motion planners. The primitives are pre-computed to meet two objective: to capture the mobility constraints of the robot as well as possible and to establish a state sampling policy that is conductive to efficient search. The first objective allows encoding mobility constraints into primitives, thereby enabling fast unconstrained search to produce feasible solutions. The second objective enables high quality (lattice) sampling of state space, further speeding up exploration during search. We further discuss several novel results enabled by using such motion primitives for kinodynamic planning, including incremental search, efficient bi-directional search and incremental sampling. Asymptotically-optimal sampling-based motion planners, like RRT*, perform vast amounts of collision checking, and are hence rather slow to converge in complex problems where collision checking is relatively expensive. This paper presents two novel motion planners, Lazy-PRM* and Lazy-RRG*, that eliminate the majority of collision checks using a lazy strategy. They are sampling-based, any-time, and asymptotically complete algorithms that grow a network of feasible vertices connected by edges. Edges are not immediately checked for collision, but rather are checked only when a better path to the goal is found. This strategy avoids checking the vast majority of edges that have no chance of being on an optimal path. Experiments show that the new methods converge toward the optimum substantially faster than existing planners on rigid body path planning and robot manipulation problems.