Robot

A robot is a programmed, actuated mechanism that performs physical tasks such as locomotion, manipulation or positioning with some degree of autonomy. Its control system belongs to the robot, alongside the mechanism. The IFR’s primary classification document reproduces this broad ISO definition and distinguishes it from the narrower definition of an industrial manipulator.^[ref]

A practical robot combines a physical mechanism, actuators, task instructions and, where required by the task, sensing and feedback control. An arm’s joint arrangement constrains the positions it can reach; a mobile mechanism must also sustain contact and balance. The degree of autonomy is a task-specific property rather than a guarantee of unrestricted reasoning or competence.

An original two-link planar arm illustrates the relationship between structure and task. For unit link lengths and joint angles $q_1,q_2$, measured with the second angle relative to the first link, forward kinematics givesAt $q_1=0$ and $q_2=\pi /2$, the endpoint is $(1,1)$; with both angles zero it is $(2,0)$. Inverse kinematics asks which joint values achieve a requested endpoint, while control must make the actual mechanism follow the intended motion.^[ref]

Reaching a geometric target is only one part of an experiment. Position error, repeatability, applied force, execution time and behavior after a disturbance measure different aspects of performance. An arm can have an accurate kinematic model yet deviate under load; a controller can compensate only within its sensing, actuation and timing limits.

The MIT Cheetah robot provides a contrasting locomotion example: perception, contact planning and force generation are coordinated while the mechanism is moving. Such examples connect the physical meaning of a robot with mechanics, geometry, computation and experimental verification of a defined task.

A quadrupedal robot is a robot with four legs used for support and locomotion. Its gait determines which feet contact the ground and when; having four legs does not imply that all four feet remain planted. Leg geometry, contact sensing and control of forces connect a desired body motion to feasible ground reactions.

An original statics calculation explains one advantage and one limitation of multiple feet. Assume point contacts on a horizontal floor, vertical gravity only, no contact moments and no acceleration. For robot mass $m$ and upward foot forces $F_i\ge 0$, force and moment balance requireHere $(x_c,y_c)$ is the vertical projection of the center of mass. Dividing by $mg$ expresses this point as a convex combination of foot locations. It must lie in their convex hull, the support polygon. A point on its boundary has no positive geometric margin against tipping in the corresponding direction.

For example, feet at $(\pm 0.50,\pm 0.30)\mathrm{m}$ surround a centered mass projection. Remove the front-left contact $(0.50,0.30)\mathrm{m}$: the origin now lies on the diagonal edge of the remaining triangle. The balance equations load the opposite two feet at $mg/2$ each and leave the third unloaded. Merely retaining three contacts has not created a positive margin. Shifting the mass projection to $(-0.10,-0.10)\mathrm{m}$ places it strictly inside that triangle, permitting three positive vertical reactions.

Dynamic running and jumping require a different balance including acceleration and angular momentum. An airborne robot has no ground support polygon at all. In the 2015 MIT Cheetah demonstration, onboard lidar estimated obstacle size and distance; control adjusted the approach strides and planned motor forces for a running jump.^[ref] The apparatus demonstrates coordinated perception and dynamic contact control, rather than a static support rule.

For a controlled walking test, record foot-contact times and body motion while changing one planned contact at a time. The geometric criterion above checks only the stipulated static model. Friction, actuator limits, terrain inclination and motion can make a geometrically supported pose physically infeasible. Conversely, a dynamic maneuver can pass through a pose that could not be maintained at rest.

The MIT Cheetah robot is an electrically actuated quadrupedal robot research platform used to investigate dynamic legged locomotion and control. Specific demonstrations must be identified by version and experiment. In the primary MIT account of a 2015 running-jump demonstration, onboard Lidar estimated obstacle height and distance, software adjusted the approach strides, and a subsequent calculation selected the jumping action.^[ref]

The experiment connects perception to physical contact. Detecting an obstacle does not by itself establish a feasible jump: the machine must reach a suitable takeoff state and supply forces within its motor and ground-contact constraints. Computation is performed while the robot approaches the obstacle, so available decision time is also a physical constraint.

An original ballistic approximation illustrates one requirement. If the center of mass must rise $\Delta h$ after takeoff, with gravity the only vertical force during flight, its launch velocity must satisfyFor $\Delta h=0.20\mathrm{m}$, this is about $1.98m/s$. If the vertical velocity starts at zero and that change is generated over $0.10\mathrm{s}$ of contact, vertical impulse balance givesThese values are illustrative requirements for the stated center-of-mass model, not measured MIT parameters. Foot clearance, body orientation, leg motion and landing cannot be inferred from this one vertical calculation.

The primary report describes tests on both a treadmill and an indoor track. The available approach distance differed, and the reported clearance success differed as well. This makes the observation conditional on apparatus and trial conditions rather than a universal performance figure.^[ref]

The scientific value of the platform is that a proposed controller has to close the loop through actual motors, contacts and sensor estimates. Successful trials demonstrate a capability in the tested conditions; robustness to other surfaces, disturbances or obstacles requires additional experiments.