Fetch is a pet game where an object, such as a stick or ball, is thrown a moderate distance away from the animal, and it is the animal's objective to grab and retrieve ("fetch") it. Many times, the owner of the animal will say "Fetch" to the animal before or after throwing the object. The game is usually played with a dog, but, in rare instances, cats (especially kittens) have been known to engage in fetch behavior.
Arizona State psychology professor Michael McBeath has proposed a simple model to explain how dogs play fetch. By mounting a camera on the head of a dog, he found that the dog changed its speed and direction in order to keep the frisbee's image in a constant position on its retina. This approach, called the linear optical trajectory, makes the frisbee appear to move in a linear path at a constant speed. McBeath had previously noticed this interception strategy in professional baseball players pursuing fly balls. [1]
Tim Pennings, [2] a mathematics professor at Hope College, has found that dogs are somehow able to calculate the optimal path to a ball thrown in the water. While playing Fetch with his Welsh Corgi, he noticed that the dog ran along the beach for a certain distance before jumping into the water. Because the dog is faster on land, this technique minimizes the total retrieval time. He showed that the dog is able to calculate the optimal point to jump into the water, a problem Pennings must resort to calculus to solve.
Perruchet and Gallego [3] have demonstrated a method for calculating this optimal path using calculus in a different way. They propose that the dog optimizes its behaviour on a moment-to-moment basis, choosing at each moment the path that allows it to maximize its speed of approach to the ball. This requires the dog to be able to accurately estimate its speed on both land and water, but does not rely on the premise that the dog plans the entire route in advance. [4]
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Jumping or leaping is a form of locomotion or movement in which an organism or non-living mechanical system propels itself through the air along a ballistic trajectory. Jumping can be distinguished from running, galloping and other gaits where the entire body is temporarily airborne, by the relatively long duration of the aerial phase and high angle of initial launch.
Dynamic programming is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics.
A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on metal–oxide–semiconductor (MOS) integrated circuit chips. They are widely used in audio signal processing, telecommunications, digital image processing, radar, sonar and speech recognition systems, and in common consumer electronic devices such as mobile phones, disk drives and high-definition television (HDTV) products.
A sheepdog trial – also herding event, stock dog trial or simply dog trial — is a competition or test of the working abilities of dogs of herding breeds. It is a type of dog sport that emerged in the 1860s in New Zealand. By the 1870s regular trials were also being held in Australia and in the United Kingdom, and by the end of the twentieth century the sport had spread to many countries of the world. In competition, dogs demonstrate basic herding management skills assessed by the judge. These events are organised by international and national cynological and sports organisations and by associations of sheep- and cattle-breeders. Usually sheep are to be herded; other animals including ducks or cows may also be used.
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.
A decision tree is a decision support recursive partitioning structure that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements.
Speed to fly is a principle used by soaring pilots when flying between sources of lift, usually thermals, ridge lift and wave. The aim is to maximize the average cross-country speed by optimizing the airspeed in both rising and sinking air. The optimal airspeed is independent of the wind speed, because the fastest average speed achievable through the airmass corresponds to the fastest achievable average groundspeed.
Disc dog is a dog sport. In disc dog competitions, dogs and their human flying disc throwers compete in events such as distance catching and somewhat choreographed freestyle catching. The sport celebrates the bond between handler and dog, by allowing them to work together. The term "disc" is preferred because "Frisbee" is a trademark for a brand of flying disc.
Dog intelligence or dog cognition is the process in dogs of acquiring information and conceptual skills, and storing them in memory, retrieving, combining and comparing them, and using them in new situations.
Clicker training is a positive reinforcement animal training method based on a bridging stimulus in operant conditioning. The system uses conditioned reinforcers, which a trainer can deliver more quickly and more precisely than primary reinforcers such as food. The term "clicker" comes from a small metal cricket noisemaker adapted from a child's toy that the trainer uses to precisely mark the desired behavior. When training a new behavior, the clicker helps the animal to quickly identify the precise behavior that results in the treat. The technique is popular with dog trainers, but can be used for all kinds of domestic and wild animals.
Trajectory optimization is the process of designing a trajectory that minimizes some measure of performance while satisfying a set of constraints. Generally speaking, trajectory optimization is a technique for computing an open-loop solution to an optimal control problem. It is often used for systems where computing the full closed-loop solution is not required, impractical or impossible. If a trajectory optimization problem can be solved at a rate given by the inverse of the Lipschitz constant, then it can be used iteratively to generate a closed-loop solution in the sense of Caratheodory. If only the first step of the trajectory is executed for an infinite-horizon problem, then this is known as Model Predictive Control (MPC).
Human–animal communication is the communication observed between humans and other animals, ranging from non-verbal cues and vocalizations to the use of language.
In optics, a caustic or caustic network is the envelope of light rays which have been reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface. The caustic is a curve or surface to which each of the light rays is tangent, defining a boundary of an envelope of rays as a curve of concentrated light. In some cases caustics can be seen as patches of light or their bright edges, shapes which often have cusp singularities.
In mathematical optimization and computer science, heuristic is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space. This is achieved by trading optimality, completeness, accuracy, or precision for speed. In a way, it can be considered a shortcut.
Betsy is a black and white longhaired Border Collie, credited with being one of the world's most intelligent dogs.
Waboba is an international outdoor toy and sporting goods brand headquartered in Stockholm, Sweden with offices in Atlanta, Georgia and Guangzhou, China. Waboba is most known for its invention of balls that bounce on water, the high bouncing Moon ball, and the Wingman silicone flying disc. The company specializes in beach and backyard toys and games. The slogan used in advertising is Keep Life Fun. The name Waboba is a registered trademark and many of its products are internationally patented.
Dog agility is a dog sport in which a handler directs a dog through an obstacle course in a race for both time and accuracy. Dogs run off leash with no food or toys as incentives, and the handler can touch neither dog nor obstacles. The handler's controls are limited to voice, movement, and various body signals, requiring exceptional training of the animal and coordination of the handler.
MCACEA is a general framework that uses a single evolutionary algorithm (EA) per agent sharing their optimal solutions to coordinate the evolutions of the EAs populations using cooperation objectives. This framework can be used to optimize some characteristics of multiple cooperating agents in mathematical optimization problems. More specifically, due to its nature in which both individual and cooperation objectives are optimize, MCACEA is used in multi-objective optimization problems.
Heuristics are simple strategies for decision making that are used to achieve a specific goal quickly and efficiently, and are commonly implemented in sports. Many sports require the ability to make fast decisions under time pressure, and the proper use of heuristics is essential for many of these decisions.
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