Snake robots can leverage their hyper-redundant morphology for both locomotion and manipulation through distributed body contact but whole-body loco-manipulation is particularly challenging since the entire body serves simultaneously as propulsive mechanism and manipulation tool Prior work on wheeled legged and snake robot platforms has decoupled these functions through dedicated appendages body segmentation or grippers We present closed-loop loco-manipulation with our snake robot COBRA without this distinction such that any part of the body may make contact We develop a contact-implicit dynamic model unifying robot-ground robot-object and object-ground interactions within a Moreau-Jean time-stepping framework and formulate a trajectory optimization over the full-order dynamics guided by a geometric planner and nominal proportional controller to autonomously push an object to a goal location during sidewinding We validate the planner and controller on hardware across varied configurations and present simulation results for a simplified trajectory optimization that resolves robot-object and object-ground contacts
Fig. 2: Full-order and reduced-order representations of the snake robot during loco-manipulation. Left: full-order model showing floating-base pose qb , joint coordinates qj , robot–ground contact impulses Λrg with friction cone Kμ , and bounding box projection pbb . Right: reduced-order planning space with robot start pose (R), box start pose (B), and goal pose (G). The robot reference trajectory qbbdes consists of an approach phase and a loco-manipulation phase. The desired box trajectory qboxdes defines the box path to the goal. The robot–box contact impulse Λrb acts at the contact point subject to friction cone Kμr .
Fig. 3: Planar free body diagram of the box. The robot applies force F at location cx on the active contact side. Ground contacts at ±l/2 exert friction forces λ1 , λ2 .
Fig. 4: Reference trajectory generation in approach mode (left) and loco-manipulation mode (right). Approach uses a second-order Bézier with a single control point c1 along the heading eθbb . Loco-manipulation uses a third-order Bézier with control points c1 , c2 along the heading and robot–box directions. Both are placed at distance ηL from their respective anchor points.
Fig. 5: Hardware loco-manipulation results. Top left: composite snapshots of a representative trial showing robot start pose (R), box start pose (B), and goal region (G). Top right: corresponding trajectory plot with reduced-order bounding box, robot center-of-mass trajectory, box trajectory, and planned Bézier path. Color gradient indicates time progression. Bottom: trajectory plots from four additional trials with varied start and goal configurations.
Fig. 6: Composite snapshots from four hardware loco-manipulation trials corresponding to the trajectory plots in Fig. 5 (bottom). The red cross marks the goal position in each trial. Faded overlays show intermediate robot and box poses.
Fig. 7: Waypoint tracking experiment and contact-implicit model validation. Top left: composite snapshots showing approach, manipulation through waypoints WP1 and WP2, and delivery to the goal region. Top right: trajectory plot with robot trajectory, box trajectory, and reduced-order bounding box. Bottom left: robot–box contact force distribution against friction cone Kμr . Bottom center: box–ground friction forces λ1 , λ2 against friction polyhedron Kμgi . Bottom right: box model validation via single shooting—simulated box trajectory overlaid on experimental trajectory with instantaneous pushing forces and ground friction forces at each time step.
Fig. 8: Reduced-order control signals during the waypoint tracking trial of Fig. 7 . Robot heading θbb , heading error θbb−θbbdes , and steering bias Δ . Vertical dashed lines mark box acquisition and waypoint transitions (WP1, WP2).
Loco-manipulation has recently shown promising capabilities; however, achieving high-precision control, managing the high-dimensional action space induced by many degrees of freedom (DoFs), and fully exploiting the inherent redundancy of whole-body systems remain challenging. In this paper, we propose a novel whole-body control framework that effectively addresses these challenges by decomposing the complex loco-manipulation problem into partial reference motion generation and low-level imitation control. We introduce a new Kinematic Normalizing Flow (KNF) model, trained on a large-scale kinematic dataset, that generates diverse partial kinematic references. A high-level controller is then trained to navigate the KNF's latent space to exploit redundant solutions, while a low-level controller learns dynamically consistent motion execution. We validate our approach on the quadrupedal robot equipped with a six-DoF robotic arm. In simulation, PAKE outperforms the evaluated baselines in tracking accuracy and feasible workspace coverage on the 4,000-target benchmark. For hardware deployment, we evaluate the system over 24 episodes across 8 different mobile loco-manipulation tasks. The system achieves end-effector pose-tracking errors of 4.5 cm and 0.14 rad, while maintaining accurate locomotion tracking with linear and angular velocity errors of 0.1 m/s and 0.01 rad/s, respectively. Our method represents a practical and powerful solution for accurate and generalized whole-body loco-manipulation in high-DoF robotic systems, with promising potential for diverse downstream robotic tasks.
Zhengmao He, Moonkyu Jung, Hyeongjun Kim +4
The Hong Kong University of Science and Technology (Guangzhou). · Korea Advanced Institute of Science and Technology. · ETH Zurich. +1
This paper presents a sim-to-real approach that enables legged robots to dynamically manipulate large and heavy objects with whole-body dexterity. Our key insight is that by performing test-time steering of a pre-trained whole-body control policy with a sample-based planner, we can enable these robots to solve a variety of dynamic loco-manipulation tasks. Interestingly, we find our method generalizes to a diverse set of objects and tasks with no additional tuning or training, and can be further enhanced by flexibly adjusting the cost function at test time. We demonstrate the capabilities of our approach through a variety of challenging loco-manipulation tasks on a Spot quadruped robot in the real world, including uprighting a tire heavier than the robot's nominal lifting capacity and dragging a crowd-control barrier larger and taller than the robot itself. Additionally, we show that the same approach can be generalized to humanoid loco-manipulation tasks, such as opening a door and pushing a table, in simulation. Project code and videos are available at https://sumo.rai-inst.com/.
Snake robots can traverse complex environments with limbless locomotion, but maneuvering in low-clearance environments remains challenging because a gait must maintain a small swept height while also providing planar steering. Existing rolling gaits preserve a low swept height body configuration but generally provide limited steering, whereas steering gaits often introduce vertical undulation and require additional clearance. With that in mind, this paper develops S-rolling, a steerable rolling gait that combines low swept height locomotion with planar maneuverability for twistable snake robots. S-rolling is designed using an S-shaped planar backbone curve, whose head and tail segments roll with independently controlled angular velocities, producing different motion modes. We derive its joint space gait equation, in which a central twist joint realizes the relative rotation between the two segments. We also develop a quasi-static kinematic model relating the segment rolling speeds to the linear and angular velocities of the robot. Real-robot experiments demonstrate the various motion modes, traversal through a 10 cm clearance test track, and maneuvering tasks beneath a large workpiece and a car chassis. In these low-clearance scenarios, S-rolling successfully performs approximately 90∘ and 180∘ heading changes, whereas the baseline rolling arc gait cannot change the robot heading.
Qingling Fan, Zhongqiang Ren
Global College, Shanghai Jiao Tong University, China