| 25 | | ==== Inverse Kinematic for 3 DoF legs ==== |
| | 25 | There are several coordinates systems involved when computing maths in order to make a robot walk; it is important to understand how they are defined. All these systems are cartesian. |
| | 26 | |
| | 27 | === Ground coordinates system === |
| | 28 | |
| | 29 | This coordinates system is attached to the ground; it is a fixed referential. |
| | 30 | |
| | 31 | * the origin is somewhere on the ground |
| | 32 | * X and Y axes define a plane parallel to the ground |
| | 33 | * Z axis points up |
| | 34 | |
| | 35 | === Robot coordinates system === |
| | 36 | |
| | 37 | This coordinates system is attached to the robot itself. |
| | 38 | |
| | 39 | * the origin is at the center of the robot |
| | 40 | * X and Y axes define a plane parallel to the ground, so that Y axis is the back-to-front axis of the robot |
| | 41 | * Z axis points up |
| | 42 | |
| | 43 | In the ground coordinates system, the robot coordinates system is just translated in the X/Y plane, and rotated arround Z. |
| | 44 | |
| | 45 | === Body coordinates system === |
| | 46 | |
| | 47 | This coordinates system is attached to the body. It is defined in the ground coordinates system. |
| | 48 | |
| | 49 | * the origin is at the center of the body |
| | 50 | * X and Y axes define a plane parallel to the body, so that Y axis is the back-to-front axis of the body |
| | 51 | * Z axis is orthogonal to X/Y |
| | 52 | |
| | 53 | This system is used to define the position of the body in the robot coordinates system, allowing it to move along the 6 DoF (3 translations, 3 rotations). |
| | 54 | |
| | 55 | === Legs coordinates systems === |
| | 56 | |
| | 57 | This coordinates systems are attached to the legs, so each leg has its own coordinates system. They are defined in the body coordinates system. |
| | 58 | |
| | 59 | * the origin is at the origin of the leg (usually the coxa joint) |
| | 60 | * X axis is along the coxa of the leg |
| | 61 | * X and Y axes are in the same plane as the one defined by the body X/Y axes |
| | 62 | * Z axis is orthogonal to X/Y |
| | 63 | |
| | 64 | To summurize, in the body coordinate system, the legs coordinates systems are just translated in the X/Y plane, and rotated arround Z. |
| | 65 | |
| | 66 | === Body/legs geometry === |
| | 67 | |
| | 68 | [[Image(body_legs.png, 500px, nolink)]] |
| | 69 | |
| | 70 | === Inverse Kinematic ==== |
| | 71 | |
| | 72 | ==== 3 DoF legs ==== |
