Robots are mechanical devices that are controlled by computer programs. Some of them act unexpectedly intelligent due to recent improvements in processing speed (hardware) and neural nets (computer science) as well as good application of differential equations (mathematics).
Differential equations are mathematical equations with a function and its derivative. So a simple differential equation is \(f(x) = f'(x)\). They are commonly used in physics, because you often have functions that have time as their argument. A simple example would be the growth of a population in biology (see Differential Equations: some simple examples from Physclips).
The Cubli is a 15 × 15 × 15 cm cube that can jump up and balance on its corner. Reaction wheels mounted on three faces of the cube rotate at high angular velocities and then brake suddenly, causing the Cubli to jump up. Once the Cubli has almost reached the corner stand up position, controlled motor torques are applied to make it balance on its corner. In addition to balancing, the motor torques can also be used to achieve a controlled fall such that the Cubli can be commanded to fall in any arbitrary direction. Combining these three abilities -- jumping up, balancing, and controlled falling -- the Cubli is able to 'walk'.
Quadcopters by Raffaello D'Andrea
In a robot lab at TEDGlobal, Raffaello D'Andrea demos his flying quadcopters: robots that think like athletes, solving physical problems with algorithms that help them learn. In a series of nifty demos, D'Andrea show drones that play catch, balance and make decisions together -- and watch out for an I-want-this-now demo of Kinect-controlled quads.
Kuka Table Tennis Robot
The unbelievably fast KUKA robot faces off against one of the best table tennis players of all time. Who has the best technique? Who will win the first ever table tennis duel of human versus robot?
Watch this thrilling commercial of table tennis and robotics performed at the highest level. The KUKA KR AGILUS demonstrates its skills with the table tennis racket - a realistic vision of what robots can be capable of in the future.
Timo Boll, the German table tennis star, is the new brand ambassador for KUKA Robotics in China. The collaboration celebrates the inherent speed, precision, and flexibility of KUKA's industrial robots in tandem with Boll's electrifying and tactical prowess in competition. To celebrate the new KUKA Robotics factory in Shanghai, the thrilling video was a highlight of the Grand Opening on March 11th, 2014. The 20,000 sq. meter space will produce the KR QUANTEC series robot as well as the KRC4 universal controller for the Asian market. As a market leader in China, KUKA aims to further develop automation in the country while providing a modern and employee-friendly working environment.
A gecko-like robot from Stanford.
A robot by Boston Dynamics that runs 45 km/h!
From the Biorobotics Lab at Carnegie Mellon University, a snake robot (Snakebot) demonstrates how it can climb a tree and look around.
Please keep in mind that this robot climbed a specific tree with a specific trunk width about 1 meter off of the ground. The researchers working to design, build and program these robots still have much work to do to get these bots to climb taller trees of various sizes and to navigate over branches and wires.
A thousand-robot swarm created by Harvard researchers can self-assemble into different shapes. Learn more: A Thousand Kilobots Self-Assemble Into Complex Shapes