UR$-10$ Pick & Place Trajectory with Gripper Orientation

My Solutions $>$

Create a UR$-10$ pick and place task space quintic trajectory. Solve inverse kinematics to ensure the UR$-10$ can kinematically follow the trajectory. Check the jacobian for this trajectory to determine how well suited the UR$-10$ is to performing this operation.

waypoint $A$ is located at $x=0\mathrm{.}7,y=0,z=0\mathrm{.}6$

waypoint $B$ is located at $x=0\mathrm{.}7,y=0,z=0$

waypoint $C$ is located at $x=0\mathrm{.}2,y=0\mathrm{.}8,z=0\mathrm{.}6$

waypoint $D$ is located at $x=0\mathrm{.}2,y=0\mathrm{.}8,z=0$

At time $0,$ the gripper begins at waypoint $A.$ The gripper then travels vertically down to an object located at waypoint $B.$ It arrives at the object at $1$ second. The gripper instanteneously grabs the object. The gripper then lifts the object vertically and arrives back to waypoint A at $2$ seconds. The gripper then carries the object, arriving at waypoint $C$ at $3$ seconds. The gripper lowers the object and arrives at waypoint $D$ at $4$ seconds. The gripper then instantaneously releases object. Finally the gripper moves vertically upward and arrives at $C$ at $5$ seconds. The gripper stops to rest $($zero velocity and zero acceleration$)$ at each waypoint along its $5$ second trajectory. The trajectory uses $0\mathrm{.}02$ second time intervals to define the trajectory time history. Gripper orientation along trejectory very important. Orientation should be a $90$ degree rotation around the y axis axang$2$tform$([010$ pi$]).$ Using the move menu on the teach pendant, UR$-10$ joints are first positioned to $[-0\mathrm{.}2-1\mathrm{.}21\mathrm{.}61\mathrm{.}9-1\mathrm{.}80\mathrm{.}0$