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Keep Rollin' - Whole-Body Motion Control and Planning for Wheeled Quadrupedal Robots
Marko Bjelonic, C. Dario Bellicoso, Yvain de Viragh, Dhionis Sako, F. Dante Tresoldi, Fabian Jenelten, Marco Hutter
TL;DR
Wheeled-legged robots aim to combine walking versatility with driving efficiency, but dynamic planning and control must account for wheel-induced degrees of freedom and contact constraints. The paper integrates online ZMP motion optimization with hierarchical whole-body control on torque-controlled ANYmal. Experiments demonstrate dynamic hybrid locomotion across varied terrain, including a speed of 4 m/s and an 83% lower cost of transport than trotting.
Problem
Existing wheeled-legged robots often do not model whole-body dynamics, wheel-related degrees of freedom, reaction forces, or torque-controlled no-slip contacts, limiting evidence for dynamic locomotion.
Method
The framework continuously optimizes ZMP-based reference trajectories and tracks them with a hierarchical whole-body controller that includes nonholonomic wheel constraints.
Results
The torque-controlled ANYmal demonstrates dynamic locomotion over flat, inclined, and rough terrain, including driving and walking over steps.
Takeaways & Limitations
The same integrated planner and controller supports hybrid locomotion that combines the mobility of legs with the efficiency of driving.
Abstract
from arXiv · showhide
We show dynamic locomotion strategies for wheeled quadrupedal robots, which combine the advantages of both walking and driving. The developed optimization framework tightly integrates the additional degrees of freedom introduced by the wheels. Our approach relies on a zero-moment point based motion optimization which continuously updates reference trajectories. The reference motions are tracked by a hierarchical whole-body controller which computes optimal generalized accelerations and contact forces by solving a sequence of prioritized tasks including the nonholonomic rolling constraints. Our approach has been tested on ANYmal, a quadrupedal robot that is fully torque-controlled including the non-steerable wheels attached to its legs. We conducted experiments on flat and inclined terrains as well as over steps, whereby we show that integrating the wheels into the motion control and planning framework results in intuitive motion trajectories, which enable more robust and dynamic locomotion compared to other wheeled-legged robots. Moreover, with a speed of 4 m/s and a reduction of the cost of transport by 83 % we prove the superiority of wheeled-legged robots compared to their legged counterparts.
I. INTRODUCTION
Wheeled-legged robots seek to combine driving efficiency with the versatility of walking, but existing systems often omit whole-body dynamics and torque-controlled wheel interaction. This paper addresses that gap with integrated planning and control for dynamic hybrid locomotion.
- Wheeled locomotion is faster and more efficient, while legged locomotion is more versatile in challenging environments.
- Most prior wheeled-legged robots use their legs as active suspension rather than as a locomotion alternative to the wheels.
- Existing approaches often omit whole-body dynamics, wheel-related degrees of freedom, contact forces, and torque control needed for robust dynamic locomotion.
- The proposed framework integrates online ZMP-based planning with hierarchical whole-body control and nonholonomic wheel constraints.
- The framework enables dynamic motions over flat, inclined, and rough terrain while supporting both driving and walking.
II. MODELLING OF WHEELED-LEGGED ROBOTS
The robot is modeled as a free-floating base with wheel-equipped legs, using generalized coordinates, velocities, dynamics, and wheel-specific contact behavior. Unlike point contacts, rolling-wheel contacts have joint-angle-dependent kinematics and nonzero contact-point acceleration.
- A wheeled-legged robot is modeled as a free-floating base with legs and wheels attached as end-effectors.
- The generalized velocity dimension is nu = 6 + nj, combining six base coordinates with the joint coordinates.
- The equations of motion include the mass matrix, Coriolis, centrifugal and gravity terms, generalized torques, support Jacobians, and contact forces.
- Wheel-fixed contact points have nonzero acceleration, unlike stationary point contacts, because rolling introduces wheel motion into the contact kinematics.
- Wheel contact acceleration depends on the wheel-frame rotation, wheel radius r0, and wheel joint angle θi.
B. Terrain and Contact Point Estimation
The system estimates a locally planar terrain and defines leg-fixed and wheel-fixed contact frames aligned with the terrain normal and wheel rolling direction. These frames distinguish stationary leg references from rolling contact behavior.
- The robot blindly locomotes on terrain locally modeled as a three-dimensional plane estimated from recent wheel-frame contact locations.
- Leg-fixed and wheel-fixed contact frames are introduced to simplify the motion controller and planner.
- Both contact frames lie at the intersection of the wheel plane and estimated terrain plane, with z aligned to the terrain normal.
- The contact-frame x-axis is perpendicular to the terrain normal and aligned with the wheel rolling direction cx.
- The leg-fixed contact point may move during contact, whereas the wheel-fixed contact Jacobian depends on the wheel joint angle θi.
III. MOTION PLANNING
Motion planning decomposes whole-body optimization into parallel modules for footholds, motion, and whole-body control. Contact schedules and support polygons organize walking and driving, while rolling enables moving footholds during driving.
- The planner simplifies complex whole-body dynamics into COM and foothold motion optimization using a ZMP model.
- Foothold, motion, and whole-body-control modules solve separate optimization problems in parallel without interrupting one another.
- Contact schedules define periodic lift-off and touch-down events, while driving keeps every leg in contact without lift-off events.
- Support polygons are generated from expected footholds and their time durations using the contact schedule.
- During driving, wheels permit trajectories along the rolling direction, making the leg-fixed contact position a moving foothold.
C. Motion Optimizer
The motion optimizer generates whole-body COM and foothold references using spline-parameterized trajectories and stacked optimization coefficients.
- The optimizer generates x, y, and z whole-body COM references from the support polygon sequence and robot state.
- The COM position, velocity, and acceleration are represented with quintic spline sequences.
- A foothold is defined as the contact position of a grounded leg.
- Each spline uses 18 coefficients collected in α_k, and all spline coefficient vectors are stacked into the optimization parameter vector.
2) Optimization problem:
The motion optimizer solves a nonlinear constrained problem whose stability requirement keeps the ZMP inside the support polygon.
- The optimization minimizes objective f(ξ) subject to equality constraints c(ξ) and inequality constraints h(ξ).
- Sequential quadratic programming solves for optimal spline coefficients continuously over a horizon of τ seconds.
- The ZMP constraint uses the gravito-inertial wrench computed from COM position, acceleration, angular momentum, robot mass, and gravity.
- The formulation constrains the ZMP position to lie inside the support polygon.
- Table I lists the costs and constraints included in the motion optimization problem.
4) Deformation of support polygons while driving:
While driving, moving wheel contacts deform the support polygon, so the planner predicts footholds and interpolates polygon edges over time.
- Driving makes contact locations and footholds nonstationary, requiring a time-varying support polygon sequence.
- The method assumes the support polygon keeps a constant number of edges, allowing one spline to describe COM motion.
- Expected foothold positions over horizon τ are computed from reference velocities assumed constant across that horizon.
- Each deformed edge is obtained by interpolating coefficients of the current and expected support polygon edges.
- The COM and wheel references are tracked by a hierarchical whole-body controller formulated as prioritized quadratic programs.
A. Prioritized Tasks
The hierarchical whole-body controller solves prioritized equality and inequality tasks for dynamics, contact feasibility, rolling, motion tracking, and wheel-specific behavior.
- Prioritized Tasks: The highlighted tasks in Table II are specifically tailored to wheeled-legged robots.
- Prioritized Tasks: The optimization enforces consistency with the floating-base equations of motion.
- Prioritized Tasks: Torque limits and friction-pyramid constraints keep actuator torques bounded and contact forces within the estimated surface friction cone.
- Prioritized Tasks: The nonholonomic rolling constraint is imposed as an equality constraint, including centripetal accelerations of contact points.
- Prioritized Tasks: COM, swing-leg, and grounded-leg operational-space references are tracked through dedicated motion tasks.
- Prioritized Tasks: Swing-wheel rotation is damped for each swing leg using a derivative-gain task based on wheel rotational speed.
- Prioritized Tasks: Grounded-leg tracking constrains acceleration along the rolling direction, while contact-force minimization reduces slippage.
B. Torque Generation
Given an optimal solution, the framework converts the optimized accelerations and contact forces into desired torques for the robot’s actuated joints.
- The controller computes desired actuation torques from the optimal solution ξ∗ and sends them to the robot.
- The torque-generation equation uses the actuated-joint dynamics and subtracts the contribution of contact forces mapped through the relevant constraint matrix.The terms Mj(q), hj(q, u), and JSj are defined as lower rows of the equations of motion relative to the actuated joints.
V. EXPERIMENTAL RESULTS AND DISCUSSION
Experiments on ANYmal evaluate combined driving and walking across indoor environments, including inclines and transitions between locomotion modes. The results show accurate tracking, constraint satisfaction, and adaptation to terrain irregularities.
- The experiments use a real quadrupedal robot with non-steerable, torque-controlled wheels, external joystick velocity inputs, and onboard computation.State estimation fuses IMU and actuator kinematics, including wheel measurements, while the WBC and estimator run at 400 Hz.
- The motion optimizer solves the nonlinear problem through sequential QP problems and runs between 100 and 200 Hz depending on the gait.
- Indoor Environment: Flat Terrain: ANYmal transitions between driving and walking during a 90 degrees turn, driving small curvatures by yawing its base despite its non-steerable wheels.For larger curvatures, the robot needs to step, demonstrating combined wheeled and legged motion.
- Indoor Environment: Inclined Terrain: Negligible tracking error results from a motion optimizer updating at up to 200 Hz and reinitializing with the robot’s measured state after every iteration.The executed COM and right-front-leg trajectories are almost identical to the optimized desired trajectories.
- Indoor Environment: Inclined Terrain: 0.7 m/s: ANYmal drives over two inclines while maintaining COM height and avoiding friction-constraint violations at the wheels.The optimized trajectories show that the COM motion is unaffected by the two obstacles.
C. Outdoor Environment: Crossing a Street
Outdoor experiments demonstrate that ANYmal combines driving and walking to cross steps and stairs, change direction, and operate dynamically without terrain perception. The reported results also include high speed and reduced transport cost.
- C. Outdoor Environment: Crossing a Street: ANYmal crosses a street by driving down one step, walking over another, and rotating its base around yaw to change driving direction.
- C. Outdoor Environment: Crossing a Street: 1 m/s: the robot drives down steps and stairs without terrain perception and drives down the stair without stepping.The experiment also illustrates walking over a step and changing direction by yawing the base.
- D. High Speed and Low Cost of Transport: 4 m/s: ANYmal exceeds its previously reported maximum speed of 1.5 m/s, while its mechanical COT is 0.1 at 2 m/s.
- D. High Speed and Low Cost of Transport: 83 %: driving lowers mechanical COT relative to the trotting gait, while the reduction relative to skating motions is 17 %.At 2 m/s, the reported mechanical power consumption is 63.64 W.
- VI. CONCLUSIONS: The framework integrates torque-controlled wheels into whole-body planning and control, using continuously updated 3D ZMP plans and hierarchical WBC with nonholonomic constraints.The paper reports dynamic motions over flat and inclined terrains and over steps.
- VI. CONCLUSIONS: Long-horizon perceptive motion planning in challenging environments remains unsolved for wheeled-legged and legged robots.