Finger: turn the spinner (small target)

The finger domain of the DeepMind Control Suite (MuJoCo), in the x-z plane (z up, no gravity). A two-link finger is mounted on a hinge at (x, z) = (-0.2, 0.4): the proximal link is 0.18 m long; the distal link ends in a rounded fingertip whose far end is 0.161 m from the distal joint (fingertip radius 3 cm). Both joints are damped and limited to +-110 degrees (+-1.92 rad). Angles are in radians: proximal_angle is the proximal link's direction measured counter-clockwise from +x in the x-z plane (0 = pointing towards +x, -pi/2 = pointing down), distal_angle the distal link's angle relative to it. The spinner is a free body on an unactuated, damped hinge at (0.2, 0.4): a bar 0.26 m long and 0.12 m wide made of two capsules, which stops turning almost at once when nothing pushes it. One end is marked: its tip (spinner_tip_pos) lies 0.13 m from the hinge. The target is a point on the same 0.13 m circle (target_pos). Only the fingertip and the proximal link collide; the finger can reach the spinner only on its left side. Simulated time advances only when you act; the scene is paused while you think. A feedback controller can run as a script: Python 3 with numpy is available, and robo observe --json / robo act ... --json print machine-readable output.

Task

Turn the spinner with the fingertip until its marked tip lies in the target circle (radius 0.03 m around (0.239, 0.524)), and leave it there. At the start the marked tip is at (0.164, 0.525), 0.075 m from the target; the finger is at rest.

Success: the spinner's marked tip inside the target circle (dist_to_target <= 0, the task's own reward condition), held for 25 consecutive steps (0.5 s of simulated time), judged by the episode server from the simulated state after every step. The episode ends as solved the moment that happens; robo done before that scores 0.

Controls. robo act PROXIMAL DISTAL [--repeat N] applies torques of 30 N m and 15 N m per unit at the proximal and distal joints, each in [-1, 1] (positive increases the joint angle), for N steps of 20 ms. There are no skills.

Observation. robo observe reports dm_control's own observation, position (the two joint angles, then the spinner tip's x and z relative to the hinge), velocity (the two joints' and the hinge's angular velocities), touch (log(1 + force) of the fingertip's two touch sensors), target_position (target relative to the hinge) and dist_to_target (distance from the tip to the target minus the target radius), plus by name: proximal_angle, distal_angle, proximal_vel, distal_vel, fingertip_pos (centre of the fingertip), fingertip_end_pos (its far end), spinner_center, spinner_angle (the hinge angle, rad), spinner_vel, spinner_tip_pos, target_pos, target_radius and tip_to_target (all positions (x, z) in m). Every task also reports reward (dm_control's own reward for the last step, for information), in_target (whether the success condition holds right now), hold_steps (for how many consecutive steps it has held) and hold_required, and time_s (simulated time). Cameras: cam0, cam1; robo observe --image [--camera C] saves a picture.

The step budget is 1000 steps (20 s of simulated time).