A humanoid has infinitely many ways to stand up from sitting while maintaining balance, making sit-to-stand (STS) a challenging control problem. We synthesise natural humanoid STS motion from scratch using reinforcement learning, without demonstrations or reference trajectories. A single Proximal Policy Optimisation policy learns smooth, human-like rising driven by three complementary components. (i) A coupled force/chair-height curriculum is used. A vertical pelvis-assist force aids early trajectory exploration and decays over training. Taller chairs are unlocked with decaying assisting force. This ensures that the policy masters a viable STS trajectory at each chair height before being exposed to harder ones, avoiding the premature distribution shift that otherwise collapses generalisation. (ii) Motion robustness is achieved by randomly sampling from a large number of inverse kinematics-generated initial and target poses spanning over eight chair heights. (iii) A set of rewards is defined inspired from biomechanics and optimal control studies. They shape the robot's angular momentum for seat-off, and enable support-region transition via centre of pressure attraction function to ensure smooth low-effort actuation. On a deterministic force-free evaluator, the policy attains more than 97% balanced-standing success across eight chair heights. The policy generalises smooth motion across chair heights and enables the robot to rise from substantially deep-seated postures as compared to the state of the art.
Figures & tables
Assist force range
Unlocked chair lanes
Fmax>100 N
{0}
80<Fmax≤100 N
{0,1}
60<Fmax≤80 N
{0,1,2,3}
40<Fmax≤60 N
{0,1,2,3,4,5}
20<Fmax≤40 N
{0,1,2,3,4,5,6,7}
Fmax≤20 N
{1,2,3,4,5,6,7}
Table 1: Assist-force and chair-height curriculum. Each lane is a discrete seat height (lane 0 lowest). New lanes are progressively unlocked as Fmax decays.
Term
Expression
Weight
Common (applied every step)
roll
exp(−10ϕ2)
1
waist yaw
exp(−10qw2)
1
foot contact
exp(−50(dℓ+dr))
1
spin
exp(−0.5(ωx2+ωz2))
1
symmetry
exp(−5∥esym∥2)
1
Table 2: Rewards and their weights. Notation: hs=1.3236 m, c : COP, cˉhull : support-hull centroid, τf : foot tilt, nb : non-foot brace contacts, esym : mirror error, Δa=at−at−1 , Δ2a=at−2at−1+at−2 , other symbols as in the text). † rise-low ( ρ<0.1 ) only, with cref=21(cb+cˉfeet) there and the hull centroid otherwise.
Run
Removed component
Success (%)
Fall (%)
Act. jit.
DoF jit.
Sτ
Sq
Energy (Joules)
tstand (s)
Full
none (reference)
97.8
2.2
1.535
0.105
1.00
0.963
115.6
3.54
Rise-frac-off
rise-fraction staging
0.0
59.3
2.522
0.059
1.00
0.187
94.80
N/A
COP-off
measured-COP shaping
97.0
3.0
3.35
0.103
1.00
0.990
115.2
3.60
Schedule-off
progressive chair unlock
85.0
15.0
1.393
0.073
1.00
0.807
116.9
3.50
Omega-off
sagittal pitch-momentum
88.0
11.8
0.64
0.045
1.00
0.882
115.5
3.66
Table 3: Ablation study: each ablation omits one system component. All policies are evaluated deterministically (force-free, 8 lanes, 50 resets per lane).
Figure 1: Learned STS motion and randomized initial poses.
Figure 2: Temporal variation of ( 2(a) ) pitch joint torques and ( 2(b) ) angles during the rising phase. The red vertical line ( ≈0.5 s) indicates seat-off while the green dashed vertical line ( ≈3.9 s) marks 90% rise completion
Figure 3: The robot transfers its balance (quantified via its COP location) from the chair (encircled point) to the centroid of the foot-only support region.