We present a planning and control approach to reactively use hand contacts to stabilize a humanoid in low stability scenarios, where only using feet contacts may result in a fall. Candidate contacts are sampled within the robot's reachable workspace, and a preview is computed by rolling out the centroidal dynamics through pre-impact, impact and post-impact phases. Sampled points are scored based on the Center of Pressure (CoP) control authority at the post-impact phase. Central to our approach is a learned model of the robot's CoP region during post-impact, which enables rapid evaluation of candidate contact points compared to traditional optimization-based methods. The presented planner has two stages: the first selects an optimal bracing region and the second computes an optimal bracing point within the region. Our simulation results demonstrate an average increase in impulse resilience of 89% over recovery without hand contacts and 17% over a naive planning strategy (closest reachable region). We validate our framework on hardware, performing push tests while standing and walking. The standing trials show an average 43% reduction in stabilization time compared to naive hand placement and the walking trials demonstrate a 18% reduction compared to baseline recovery (without hand contacts).
Figures & tables
Fig. 1 : (left) Alex reactively bracing against a wall to stabilize after being pushed while walking. (right) The robot’s head-mounted depth sensor detects the bracing surface (blue) and the robot’s feasible CoP region (red) is previewed to select a bracing point.
Fig. 2 : (Left) Example multi-contact scenario in which the robot has two feet and two hand contacts. The robot can feasibly place the CoP in the red convex region, which is computed through successive evaluations of Eq. ( 2 ). (Right) We train a neural network to learn the ri , the additional CoP control authority along query direction i given by the hand contacts.
Fig. 3 : Depiction of the 5 modeled contact permutations for mixed hand and feet contacts, in which at least 1 foot and 1 hand are in contact. The resulting CoP region is shown in red for each example configuration. We train a distinct network to learn the CoP region of each contact configuration.
Fig. 4 : Left: Contact states considered in this work their feature dimension, ∗ note there are two single-handed, single-foot states to cover contact on the same and opposites sides as the stance foot. Right: Neural network architecture which computes the vector r , describing the additional CoP control given by the hand contacts.
Fig. 5 : Centroidal-based evaluation of a sampled contact point. The predicted capture point trajectory ξpred is propagated, starting at the time of planning t=0 , through impact, t=T . The feasible multi-contact CoP region is used to compute an optimal post-impact CoP, x∗ . The contact point’s score s is computed to represent the CoP control authority at post-impact.
Fig. 6 : Control flow of our reactive bracing framework. Candidate bracing planar regions are extracted from a head-mounted depth camera. The planning thread is triggered if sufficiently high capture point tracking is detected, which first computes an optimal bracing region per-side, by sampling each region once, and then computing an optimal contact point within the region, by sampling multiple times in the region. The planner dispatches the plan to the controller, which makes contact until sufficiently high stability is regained.
Fig. 7 : Points in the optimal bracing surface are sampled and scored using a centroidal rollout (Sec. IV-B ). The optimal brace point p∗ is computed through a QP that models the score gradient and regularizes on the closest reachable point (Sec. IV-D ). Here, the region color depicts the cost function of the QP.
Contact config.
ermse [cm]
Single foot, single hand (same side)
1.36
Single foot, single hand (opposite side)
1.06
Dual foot, single hand
0.89
Single foot, dual hand
2.21
Dual foot, dual hand
2.62
TABLE I : Neural Network Evaluation
Fig. 8 : Three scenarios were tested in simulation. In each, we determine the maximum sustainable impulse for (i) no bracing, (ii) naive (closest reachable) bracing, and (iii) bracing using the presented planner.
Scenario
No
Naive
Optimized
Bracing
Bracing
Bracing
Standing, For. Push
15.6
25.8
29.4
Walk Sideways, For. Push
17.7
36.4
42.3
Walk Backwards, For. Push
23.0
26.6
32.1
TABLE II : Maximum Sustainable Impulse [N ⋅ s]
Numerical
Neural
Optimization
Network
CoP Region (per rollout)
0.65 ms
0.13 ms
IK (per rollout)
13 ms
-
Additional computation (per side)
3 ms
Total (2 sides, 14 rollouts/side)
388 ms
9.7 ms
TABLE III : Planner Benchmark
Fig. 9 : We tested our planner in the scenario shown, where the robot has two available regions to brace with the left hand: a vertical wall in front and a slanted surface on the side. The solid markers indicate the average time and corresponding capture point error when impact is detected.