Lift the ball

You control a right LEAP Hand (MuJoCo Menagerie model leap_hand, MIT: 16 joints, each driven by its own position actuator; index, middle and ring fingers have mcp, rot (side-to-side), pip and dip joints, the thumb has cmc, axl, mcp and ipl). Like a hand in a lab setup that is carried by a robot arm or gantry, it hangs from a 6-axis positioner above a table: three linear axes move the wrist in x, y and z and three rotary axes turn it in yaw, pitch and roll. The hand is not fixed to anything else and has no other support. World frame in metres: +x forward (away from the positioner's home), +y to the left, +z up; the floor is at z = 0 and the table top is at z = 0.40, spanning x from -0.35 to 0.55 and y from -0.35 to 0.35. At roll = pitch = yaw = 0 the palm faces down and the fingers point along +x. PITCH tips the fingers down (+) or up (-); ROLL turns the hand about its own long axis (+90 makes the palm face +y, 180 makes it face up); YAW turns it about the vertical (counter-clockwise seen from above is +). hand.palm_pos is a point about 3.5 cm in front of the palm, roughly where a grasped object sits. Objects are real rigid bodies with rubber-like friction: a grasp holds only as long as the fingers' contact forces and friction hold it, and anything dropped falls. An object that falls to the floor fails the task.

Task

A 6.6 cm ball (60 g) rests in a small ring stand on the table at about (0.12, 0.04). Pick it up and hold it at least 15 cm above the table top.

Success: the ball's centre is at least 0.15 m above the table top (z >= 0.55), the ball touches the hand and not the table, and it moves slower than 5 cm/s. Judged by the episode server from the simulated state after you call robo done and the hand has held still (zero action) for 10 steps.

Controls. robo act takes 22 numbers, each in [-1, 1], applied for one 40 ms step (--repeat N holds them for N steps): first the wrist group wrist.pose_delta = DX DY DZ DROLL DPITCH DYAW, which moves the positioner's target by x 1 cm along world x, y, z and by x 4 degrees on its roll, pitch and yaw joints (rotations about the wrist); then the hand group hand.joints = if_mcp if_rot if_pip if_dip mf_mcp mf_rot mf_pip mf_dip rf_mcp rf_rot rf_pip rf_dip th_cmc th_axl th_mcp th_ipl (16 values), each added to that actuator's position target as a fraction of its range (x 10 %; for the flexion joints + curls the finger). All zeros holds the current targets. The positioner is a stiff joint-space PD controller with force limits (200-300 N, 40 N m), so pushing into the table or an object stalls it instead of passing through; its target never runs more than 3 cm / 15 degrees ahead of the measured pose. The hand's actuators are the upstream position servos, so a finger stopped by an object keeps squeezing with a force that grows with the remaining target error. Skills (robo info lists arguments): move_to X Y Z [SPEED] and move_by DX DY DZ [SPEED] (straight line of the palm point, orientation kept, SPEED 0.01-0.25 m/s; reports blocked if stopped, remaining_m if it ran out of steps), rotate ROLL PITCH YAW [SPEED] (absolute positioner angles in degrees, turning about the palm point, SPEED 5-100 deg/s), turn_about X Y DEG [SPEED] (swing the hand about a vertical line, yawing with it, SPEED 5-90 deg/s; reports remaining_deg if it ran out of steps), grasp power|pinch|tripod (close those fingers until they stall or are fully closed; reports which fingers touch what), open, pose NAME (named postures: open, flat, relaxed, point, fist, power_ready, pinch_ready, tripod_ready), set_joint NAME DEG and wait [SECONDS]. Skills are plain controllers: a grasp can slip or miss, and nothing is attached to the hand.

Observation. robo observe reports hand (wrist_pos and wrist_rpy_deg of the positioner flange, their targets, palm_pos, palm_normal, finger_dir, fingertips positions, joints names with joint_pos_norm and joint_target_norm in [-1, 1] over each actuator's range, and contacts per finger), objects (position and what each touches, plus per-object details), table, landmarks (fixed things in the scene), progress and safety_events. Cameras: front (default), side, top and back.

The step budget is 700 steps (28 s of simulated time).