This paper presents a geometry-aware predictive control framework for bipedal obstacle crossing across walking and running regimes. The proposed approach integrates a phase-structured trajectory generator with a constrained model predictive control (MPC) tracking layer to generate coordinated pelvis and swing-foot motions during obstacle traversal. The crossing process is represented through five interpretable phases: pre-crossing, leading-leg clearance, straddle, trailing-leg clearance, and recovery. Within this structure, swing-foot elevation is adapted as a function of obstacle height, while lateral stance widening and pelvis repositioning are introduced as functions of obstacle depth to improve transverse clearance and body alignment. A continuous gait-parameter evolution enables smooth walk-to-run transition without discrete controller switching. The generated references are tracked using MPC to regulate motion smoothness, clearance feasibility, touchdown behavior, and lateral admissibility. The framework is evaluated in reduced-order simulation over five progressively difficult obstacles under walking and running conditions. The robot successfully crosses the first four obstacles, achieving minimum body-obstacle clearances of 0.036, 0.036, 0.059, and 0.017 m, respectively. The fifth and most demanding obstacle leads to collision, identifying the current operating boundary of the proposed reduced-order formulation. Overall, the method provides a compact, interpretable, and computationally efficient basis for intelligent obstacle-aware bipedal locomotion.
Figures & tables
Fig. 1 : Geometry-aware reference generation and constrained predictive tracking for phase-structured obstacle crossing.
Obs.
Regime
Pos. (m)
Height (m)
Speed (m/s)
Cmd. apex (m)
Half stance (m)
O1
Walk
4.0
0.18
0.75
0.266
0.120
O2
Walk
6.8
0.34
0.75
0.458
0.120
O3
Run
10.4
0.48
1.28
0.675
0.120
O4
Run
13.2
0.66
1.28
0.898
0.120
O5
Run
16.2
0.90
1.28
1.196
0.120
TABLE I : Obstacle configuration and commanded crossing references.
Fig. 2 : Front-view crossing sequence for O1 in walking mode, showing the five-stage progression with a commanded foot apex of 0.266m .
Fig. 3 : Front-view crossing sequence for O2 in walking mode. The foot apex increases to 0.458m , while the commanded peak half-stance width remains identical to O1.
Fig. 4 : Front-view crossing sequence for O3 in running mode. The ordered crossing stages are maintained at an active crossing speed of 1.28m/s .
Fig. 5 : Front-view crossing sequence for O4 in running mode. This is the tallest successfully crossed obstacle in the reported sequence, with minimum sampled clearance 0.017m .
Fig. 6 : Attempted O5 crossing in running mode. Collision occurs before the intended swing apex is attained; the snapshots alone do not isolate the initiating failure mechanism.
Fig. 7 : Global simulation diagnostics: (a) vertical pelvis and foot trajectories; (b) minimum signed obstacle clearance, locomotion speed, and collision indicator.
Fig. 8 : Joint-angle evolution over the locomotion sequence. The reported maximum knee flexion increases across the successful O1–O4 encounters.
Obs.
Regime
Min. clr. (m)
Peak foot (m)
Max knee ( ∘ )
Outcome
O1
Walk
0.036
0.266
63.5
Success
O2
Walk
0.036
0.458
95.9
Success
O3
Run
0.059
0.671
110.0
Success
O4
Run
0.017
0.898
130.8
Success
O5
Run
-0.001
0.230
52.7
Failure
TABLE II : Reported obstacle-wise crossing outcomes.
This paper presents a multi-phase whole-body model predictive control (MPC) approach for bipedal walking, combining a detailed whole-body model in the near horizon with a simplified single-rigid-body model in the later prediction steps. This reduces computational complexity while retaining prediction capabilities. The resulting nonlinear optimal control problem is solved entirely within the general-purpose, off-the-shelf nonlinear MPC framework acados, using sequential quadratic programming (SQP). Given a contact schedule and a target walking speed, the controller optimizes joint torques without depending on preselected footstep locations. The controller is validated in MuJoCo simulation on the 18-DoF bipedal robot HyPer-2.
Franek Stark, Felix Wiebe, Shubham Vyas +2
Robotics Innovation Center at the German Research Center for Artificial Intelligence (DFKI), Bremen, Germany · University Bremen, Germany
This paper presents Residual Koopman MPC (RK-MPC), a Koopman-based, data-driven model predictive control framework for quadruped locomotion that improves prediction fidelity while preserving real-time tractability. RK-MPC augments a nominal template model with a compact linear residual predictor learned from data in lifted coordinates, enabling systematic correction of model mismatch induced by contact variability and terrain disturbances with provable bounds on multi-step prediction error. The learned residual model is embedded within a convex quadratic-program MPC formulation, yielding a receding-horizon controller that runs onboard at 500 Hz and retains the structure and constraint-handling advantages of optimization-based control. We evaluate RK-MPC in both Gazebo simulation and Unitree Go1 hardware experiments, demonstrating reliable blind locomotion across contact disturbances, multiple gait schedules, and challenging off-road terrains including grass, gravel, snow, and ice. We further compare against Koopman/EDMD baselines using alternative observable dictionaries, including monomial and SE(3)-structured bases, and show that the residual correction improves multi-step prediction and closed-loop performance while reducing sensitivity to the choice of observables. Overall, RK-MPC provides a practical, hardware-validated pathway for data-driven predictive control of quadrupeds in unstructured environments. See https://sriram-2502.github.io/rk-mpc for implementation videos.
Sriram S. K. S. Narayanan, Umesh Vaidya
Department of Mechanical Engineering, Clemson University, Clemson, SC 29630, USA
In this letter, we present a hierarchical control framework that enables wheeled bipedal robots to perform planar object sliding tasks with their wheeled legs. The proposed approach formulates a nonlinear model predictive controller (NMPC) based on a reduced-order three rigid bodies (TRB) dynamical model that explicitly accounts for the hip roll degree of freedom and multiple wheel-environment contact modes, which is essential for lateral stepping and pedipulation tasks. Within this framework, the NMPC simultaneously regulates robot locomotion and interaction forces, allowing the robot to stably execute both rolling and object manipulation behaviors. A trajectory-optimization-based robot-object motion planner is developed to generate reference motions that incorporate stick-slip transitions in ground-object contact. Two representative pedipulation motions, namely scooting and lateral sliding, are validated through real-world hardware experiments, in which the robot successfully retrieves a 1 kg object from under a desk and slides a 4 kg object over a distance of 0.228 m via scooting.
Yue Qin, Yulun Zhuang, Zelin Shen +1
Department of Robotics, University of Michigan, Ann Arbor, MI 48109, USA