Motion planning

src: www.cs.rutgers.edu

Motion planning (also known as the navigation problem or piano drive issue ) is a term used in robotics for the process of degrading a task movement into a discrete motion that meet the restrictions of movement and may optimize some aspects of movement.

For example, consider navigating mobile robots inside a building to a distant street point. It should carry out this task while avoiding the wall and not falling down the ladder. The motion planning algorithm will take a description of these tasks as inputs, and generate speed and alter the commands sent to the robot wheel. Motion planning algorithms can overcome robots with larger number of joints (eg industrial manipulators), more complex tasks (eg object manipulation), different constraints (eg cars that can only push forward), and uncertainty (eg imperfect models from environment or robot).

Motion planning has several robotic applications, such as autonomy, automation, and robot design in CAD software, as well as applications in other fields, such as digital character animation, video games, artificial intelligence, architectural design, robotic surgery, and studies of biological molecules.

Video Motion planning

Drafts

The basic motion planning issue is to produce a continuous movement that connects the initial configuration S and destination G configuration, while avoiding collisions with known obstacles. Robots and obstacle geometry are depicted in 2D Ã¢ â‚¬ <Ã¢ â‚¬ workspace , while motion is represented as a path in the configuration space (maybe higher-dimensional).

Configuration space

A configuration describes a robotic pose, and C's configuration space is the set of all possible configurations. As an example:

If the robot is a single (zero-sized) point that translates into a 2 dimensional (workspace) field, C is a field, and the configuration can be represented using two parameters (x, y).
If the robot is a 2D form that can translate and rotate, the workspace is still 2 dimensional. However, C is a special Euclidean group SE (2) = R ² ${\ displaystyle \ times}$ SO (2) is a special orthogonal group of 2D rotations ), and the configuration can be represented using 3 parameters (x, y,?).
If the robot is a solid 3D shape that can translate and rotate, the workspace is 3 dimensional, but C is a special Euclidean group SE (3) = R ³ ${\ displaystyle \ times}$
If the robot is a fixed-base manipulator with N revolute joints (and no closed loop), C is an N-dimension.

A collection of configurations that avoid collisions with obstacles is called free C _space. Complementary C _free in C is called a constraint or restricted area.

Often, it is difficult to explicitly calculate the form of C _{for free}. However, test whether the configuration provided in C _free is efficient. First, advanced kinematics determine the position of robot geometry, and collision detection tests if the robot geometry collides with environmental geometry.

Target space

The target space is the linear part space of the free space that indicates where we want the robot to move to. In global motion planning, the target space can be observed by the robot sensor. However, in local motion planning, the robot can not observe the target space in some states. To solve this problem, the robot passes through several virtual target spaces, each located within the observable area (around the robot). The virtual target space is called a sub-destination.

Maps Motion planning

Algorithm

Low dimensional problems can be solved by grid-based algorithms that line the grid above the configuration space, or geometric algorithms that calculate the form and connectivity of C _{for free}.

Appropriate motion planning for high-dimensional systems under complex constraints is computationally difficult to solve. Potential terrain algorithms are efficient, but fall prey to local minima (exceptions are potential areas of harmony). Sampling-based algorithms avoid local minimum issues, and solve many problems quickly. They can not determine that there is no way, but they have a probability of failure that drops to zero as more time is spent.

Current sampling-based algorithms are considered sophisticated for motion planning in high-dimensional spaces, and have been applied to problems that have dozens or even hundreds of dimensions (robot manipulators, biological molecules, animated digital characters, and robotic legs).

Network-based search

The grid-based grid overlay approach to the configuration space, and assume each configuration is identified with the grid point. At each grid point, robots are allowed to move to adjacent grid points as long as the line between them is fully contained in C _free (this is tested by collision detection). It discretizes sets of actions, and search algorithms (such as A *) are used to find paths from start to destination.

These approaches require a grid resolution setting. Search is faster with grid rough, but algorithm will fail to find path through narrow section of C _free. In addition, the number of points in the grid grows exponentially in the configuration space dimension, which makes it unsuitable for high-dimensional problems.

Traditional grid-based approaches produce paths that alter the canopy are restricted to a multiple of the given base angle, often resulting in suboptimal paths. Each roadside planning approach finds shorter paths by disseminating information along the edge of the network (for fast searching) without restricting its path to the edge of the grid (to find short paths).

Network-based approaches often need to search repeatedly, for example, when knowledge of robots about changes to the configuration space or the configuration space itself changes during the course of the path. The supplementary heuristic search algorithm is quickly reproduced by using experience with the same previous path planning problem to speed up their search for the current one.

Interval-based search

These approaches are similar to the grid-based search approach except that they produce paving that covers the full configuration space, not the grid. Paving is decomposed into two subpavings X ^-, X made with boxes like X ^-? C _free? X . Characterizes the number of C _free to solve the inversion set problem. Interval analysis can be used when C _free can not be explained by linear inequality to have a secured enclosure.

Such robots are allowed to move freely in X ^-, and can not go outside X . For both subpavings, neighboring graphics are constructed and paths can be found using algorithms such as Dijkstra or A *. When a path is feasible in X ^-, it is also feasible in C _{for free}. When there is no way in X from one initial configuration to the destination, we have a guarantee that there is no viable path in C _{for free}. As for the grid-based approach, the interval approach is not appropriate for high-dimensional problems, due to the fact that the number of boxes to be generated grows exponentially with respect to the configuration space dimension.

An illustration is provided by three images on the right where a hook with two degrees of freedom must move from left to right, avoiding two small horizontal segments.

Decomposition with subpavings using interval analysis also makes it possible to characterize the free C _{topology as counting the number of connected components.}

Geometric algorithm

Show robots among polygonal obstacles

Visibility graphs
Cell decomposition

Translating objects between obstacles

Minkowski sum

Reward-based algorithm

The reward based algorithm assumes that robots in each state (internal position and state, including direction) can choose between different actions (motion). However, the outcome of any action is uncertain. In other words, the result (displacement) is partially random and partly under the control of the robot. The robot gets a positive reward when reaching the target and gets a negative prize if it collides with an obstacle. The algorithm tries to find a path that maximizes future cumulative rewards. Markov decision making process (MDP) is a popular mathematical framework used in many prize based algorithms. The advantage of MDP over other reward-based algorithms is that they produce an optimal path. The disadvantage of MDP is that they limit the robot to choose from a limited set of actions. Therefore, the path is not smooth (similar to grid-based approach). The Fuzzy Markov decision process (FDMPs) is an MDP extension that produces a smooth path using a fuzzy inference system.

Field of artificial potential

One approach is to treat the robot configuration as a point (usually electrons) in a potential field that combines attraction to destination, and repulsion from obstacles. The resulting path is output as the path. This approach has advantages because the path is generated with little calculation. However, they can be trapped in local minima from potential fields, and fail to find their way. The artificial potential field can be achieved by a direct equation similar to an electrostatic potential field or can be driven by a set of linguistic rules. In addition to being adapted as a motion planning strategy, the Artificial Potential Field is also used as an integrated risk assessment and pathway. a planning strategy to measure the carrier vehicle or threat the robot and create a reference path.

Algoritma berbasis sampling

The sampling-based algorithm represents the configuration space with the sample configuration path map. The basic algorithm samples N configurations in C, and retains them in C _{for free} to use as milestones . A roadmap is then constructed which links the two milestones of P and Q if the line PQ segment is really in C _free. Again, collision detection is used to test inclusion in C _{for free}. To find paths connecting S and G, they are added to the roadmap. If the road on the roadmap connects S and G, the planner succeeds, and returns the path. Otherwise, the reason is uncertain: there is no path in C _free, or the planner does not quite follow the milestone.

This algorithm works well for high-dimensional configuration space, because unlike combinatorial algorithms, the running time is not (explicitly) exponentially dependent on the C dimension. They are also (generally) much easier to implement. They are probabilistically complete, which means the probability that they will produce a solution close to 1 because more time is spent. However, they can not determine whether there is no solution.

Under the condition of basic in C _free, it has been proven that as the number of N configurations increases, the probability that the above algorithm finds the solution close to 1 exponentially. Visibility does not explicitly depend on the dimension C; it is possible to have high-dimensional spaces with "good" visibility or low-dimensional space with "poor" visibility. The experimental success of a sample-based method shows that the most viewed spaces have good visibility.

There are many variants of this basic scheme:

It's usually quicker to just test the segments between the closest pair of milestones, rather than all pairs.
Uneven distribution sampling attempts to place more milestones in areas that improve road map connectivity.
Quasirandom samples typically produce better configuration space than pseudorandom space, although some recent work states that the effect of random sources is minimal compared to the sampling distribution effect.
It is possible to substantially reduce the number of milestones required to solve a given problem by allowing a curved eye view (eg by crawling on obstacles blocking the path between two milestones).
If only one or more planning questions are required, it is not always necessary to build an entire space map. The tree-growing variant is usually faster for this case (one-query planning). Roadmap is still useful if many questions have to be done on the same space (multi-query planning)

List of famous algorithms

A *
D *
Parse random trees quickly
Probabilistic roadmap

Distance Metric Learning for RRT-Based Motion Planning with ...

src: i.ytimg.com

Completeness and performance

A movement planner is said to be complete if the planner in a limited time either produces a solution or correctly reports that it does not exist. The most complete algorithm is geometry based. The performance of a complete planner is judged by its computing complexity.

Completeness of resolution is a property guaranteed planner to find a way if the underlying grid resolution is good enough. Most full-resolution planners are grid-based or interval-based. Computational computing of the complete planner resolution depends on the number of points in the underlying grid, which is O (1/h ^d), where h is the resolution (the length of one side of the cell grid) and d is the dimension of the configuration space.

is a property that since more "work" is done, it is likely that the planner failed to find the path, if any, asymptotically close to zero. Several sample-based methods are fully probabilistic. The performance of a complete probabilistic planner is measured by the rate of convergence.

Incomplete planners do not always generate a viable path when they exist. Sometimes incomplete planners work well in practice.

src: marius.sucan.ro

Variant problem

Many algorithms have been developed to deal with these basic problem variants.

Differential limits

Holonomic

Manifest arm (with dynamics)

Nonholonomist

Car
Unicycles
Planes
Restricted acceleration system
Move the obstacle (time can not be backed up)
Bevel-tip steerable needle
Differential Drive Move

Optimality limits

Hybrid system

The hybrid system is a system that combines discrete and sustainable behavior. Examples of such systems are:

Robot manipulation
Mechanical assemblies
The legged robot drive
Reconfigurable robots

Uncertainty of movement
Information is missing
Active sensing
Uncensored planning

A Novel RRT Extend Function for Efficient and Smooth Mobile Robot ...

src: i.ytimg.com

Apps

Robot navigation
Automation
Car without driver
Robotic surgery
Digital character animation
Fold the protein
Security and accessibility in computer-assisted architecture design

Motion Planning | Algorithms & Applications Group

src: parasol.tamu.edu

References

Gepetto Team Members/Florent Lamiraux Nonholonomic

src: homepages.laas.fr

External links

"Open Automated Automatic Robotics Environment", http://openrave.org/
Jean-Claude Latombe talks about his work with robots and motion planning, April 5, 2000
"Open Motion Planning Library (OMPL)", http://ompl.kavrakilab.org
"Motion Strategy Library", http://msl.cs.uiuc.edu/msl/
"Motion Planning Kit", http://ai.stanford.edu/~mitul/mpk
"Simox", http://simox.sourceforge.net
"Motion Planning and Robot Control", http://www.laas.fr/~jpl/book.html

Source of the article : Wikipedia

Motion planning

Kamis, 28 Juni 2018

Motion planning

Video Motion planning