Table 3: Definition of reward terms across training stages. The per-step reward is
Δt∑iwiri , where
Δt is the control timestep and
wi are the weights listed below. Grey cells denote inactive terms. Reference-tracking terms apply only to reference-anchored environments; terms marked † apply only to goal-reaching environments. The Stage 2 contact weights use
ηrew=ηrew(u) , the reward-annealing coefficient defined in ( 3 ). The index
b runs over the nine contact bodies,
j over the 23 controlled joints, and
f over monitored contact-sensor links. Superscripts
ref denote instantaneous reference quantities;
B and
W denote body-yaw and world coordinates. Actual and reference body-yaw positions use their respective base poses.
θe is the angular difference between actual and reference base orientations,
χmov=\mathds1[∥vb∗∥>0.1] , and
mb indicates a nonzero, occupancy-gated planner target.
cbmeas indicates a vertical contact-force magnitude exceeding
1N within the sensor-history window.
wrapπ wraps angular differences to
[−π,π) . The kernel scales are
σp=0.5 ,
σr=1 ,
σv=1 ,
σω=3 ,
σq=2 ,
σq˙=10 , and
σc=1 , in the corresponding SI units. For goal rewards,
gxy=\mathds1[dg<0.5] ,
gh=\mathds1[∣Δz∣<0.2] ,
gψ=\mathds1[∣Δψ∣<0.5] , and
gv=\mathds1[v→g>0.1]\mathds1[∥vb,xyW∥≤vmax] . Here,
dg is the horizontal goal distance,
Δz is the target base height minus the current base height,
Δψ is the target-heading error, and
v→g is the horizontal velocity projected toward the goal. The speed cap is
0.8ms−1 on the configured stair terrains and
2.0ms−1 elsewhere. For get-up terrains,
gz=\mathds1[vb,zWsign(Δz)>0.1∨∣Δz∣<0.2] ; otherwise,
gz=1 .
dfoot is the fraction of feet without measured contact,
dtilt=1−(gzbase)2 uses the vertical component of projected gravity, and
dq=231∑j∣qj−q0,j∣ .
Ti denotes the terrain mask for style term
i .
Ff,xymax and
Ff,zmax are the maximum horizontal force magnitude and vertical force over the sensor-history window;
tfcontact is the continuous contact duration.
gtorso is gravity projected into the torso frame. Computed and applied torques are taken before and after actuator limiting, respectively.
[x]+=max(x,0) , and joint bounds are the configured soft limits. All thresholds use SI units.