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An Open Torque-Controlled Modular Robot Architecture for Legged Locomotion Research
Felix Grimminger, Avadesh Meduri, Majid Khadiv, Julian Viereck, Manuel Wüthrich, Maximilien Naveau, Vincent Berenz, Steve Heim, Felix Widmaier, Thomas Flayols, Jonathan Fiene, Alexander Badri-Spröwitz, Ludovic Righetti
TL;DR
The paper addresses the difficulty of conducting legged-locomotion research with costly, complex, and poorly reproducible hardware. It presents an open-source modular torque-controlled robot architecture and evaluates its impedance and motion-tracking capabilities. The system achieves dimensionless leg stiffness of 10 while supporting dynamic motions and robustness to environmental uncertainty.
Problem
Legged-robot control research lacks hardware that is inexpensive, reproducible, mechanically simple, and suitable for advanced torque, impedance, and force control.
Method
The authors combine a low-ratio brushless actuator module, multidirectional impact-tolerant foot sensor, modular 2.2 kg quadruped, impedance control, and kino-dynamic motion tracking in an open-source platform.
Results
Dimensionless leg stiffness reached 10 in experiments, while the quadruped tracked jumping and walking plans and balanced on moving platforms without environmental knowledge.
Takeaways & Limitations
The open-source, lightweight system lowers the barrier to dynamic legged-robot research and can be reproduced, compared, and improved by other laboratories.
Abstract
from arXiv · showhide
We present a new open-source torque-controlled legged robot system, with a low-cost and low-complexity actuator module at its core. It consists of a high-torque brushless DC motor and a low-gear-ratio transmission suitable for impedance and force control. We also present a novel foot contact sensor suitable for legged locomotion with hard impacts. A 2.2 kg quadruped robot with a large range of motion is assembled from eight identical actuator modules and four lower legs with foot contact sensors. Leveraging standard plastic 3D printing and off-the-shelf parts results in a lightweight and inexpensive robot, allowing for rapid distribution and duplication within the research community. We systematically characterize the achieved impedance at the foot in both static and dynamic scenarios, and measure a maximum dimensionless leg stiffness of 10.8 without active damping, which is comparable to the leg stiffness of a running human. Finally, to demonstrate the capabilities of the quadruped, we present a novel controller which combines feedforward contact forces computed from a kino-dynamic optimizer with impedance control of the center of mass and base orientation. The controller can regulate complex motions while being robust to environmental uncertainty.
I. INTRODUCTION
The paper proposes an open-source, modular torque-controlled legged robot architecture designed to make dynamic locomotion research easier to reproduce and compare. It combines inexpensive 3D-printed and off-the-shelf hardware with a lightweight quadruped, foot sensing, impedance control, and kino-dynamic motion tracking.
- Advanced legged-robot control research is hindered by costly, mechanically complex, difficult-to-compare, and often unavailable hardware.
- Open-source platforms can accelerate research by enabling direct comparison across laboratories and easier reproduction of robot systems.
- The architecture favors off-the-shelf components, plastic 3D printing, miniature sensors, efficient microcontrollers, and modern battery technologies to reduce precision machining.
- Lightweight, inexpensive robots can be operated by one researcher in smaller spaces while reducing repair, maintenance, and learning-experiment costs.
- The system includes a low-complexity torque-controlled actuator, an under-10 g multidirectional impact-tolerant foot sensor, a 2.2 kg quadruped, and a kino-dynamic-motion torque controller.
II. PLATFORM AND ROBOT OVERVIEW
The platform is built around a low-ratio brushless actuator module and supporting electronics intended for torque and impedance control. The actuator uses a compact 3D-printed package, while the electronics provide high-rate dual-motor control.
- The actuator module combines a 300KV brushless motor, 9:1 dual-stage timing-belt transmission, optical encoder, and 5000-count code wheel inside a lightweight 3D-printed shell.
- The low transmission ratio provides reasonable peak joint torque and high joint velocity while supporting torque-control transparency.
- The experimental electronics use TI evaluation boards with two BLDC booster cards and execute dual-motor field-oriented torque control at 10 kHz.
B. Foot Contact Sensor
The robot’s leg and quadruped are assembled from modular brushless actuators, a multidirectional foot-contact switch, and printable structural components. The resulting quadruped is lightweight, compact, and designed for dynamic locomotion.
- B. Foot Contact Sensor: The foot sensor detects contact at low force and withstands substantial impacts across a 270° sensing range for unpredictable terrain contacts.
- B. Foot Contact Sensor: The contact switch uses an LED and light sensor separated by a spring-loaded mechanical aperture.
- C. 2-DOF Leg and Quadruped Robot Solo: A 2-DOF leg uses two identical brushless actuator modules, a lower leg, and a distally mounted foot contact sensor.
- C. 2-DOF Leg and Quadruped Robot Solo: Solo consists of four identical legs and a 3D-printed body, weighs 2.2 kg, and has eight sagittal-plane degrees of freedom.
- C. 2-DOF Leg and Quadruped Robot Solo: The robot has approximately 24 cm standing hip height, 34 cm maximum hip height, and folds to 5 cm in height.
D. Communication and Control Software
The control stack connects the robot to a real-time PC through wired or wireless interfaces and supports multi-motor sensing and control. Experiments use a 1 kHz sensing-control loop to evaluate impedance and track optimized locomotion plans.
- D. Communication and Control Software: The ESP32-based master board routes communication between the control computer, up to eight dual motor drivers, and additional sensors.
- D. Communication and Control Software: The system supports Ethernet and WiFi communication, achieving 200 µs wired round-trip time and approximately 1100 µs wireless round-trip time with about 4% packet loss.
- D. Communication and Control Software: A real-time Ubuntu PC runs the sensing-control loop at 1 kHz and provides CAN, Ethernet, and WiFi interfaces through a C++ API with Python bindings.
- D. Communication and Control Software: Experiments quantify impedance regulation and test quadruped tracking of kino-dynamically optimized motions.
A. Impedance control of the 2-DOF leg
The leg regulates foot impedance through Cartesian stiffness and damping control using motor current and position measurements, without force feedback. Quasi-static tests show broad stiffness regulation, near-linear force–displacement behavior, and saturation-related errors at higher commands.
- Experimental setup: The test stand combined a linear guide, a 6-axis force sensor for ground reaction forces, and a string potentiometer for leg height.These external sensors were used to validate impedance control quality.
- Quasi-static regulation: 20–360 N/m: desired leg stiffness was regulated during slow motion without damping.Higher stiffness caused instability without damping; small damping could increase the maximum stiffness, though this was not shown.
- Quasi-static regulation: The controller maintained a near-linear relationship between vertical ground reaction force and leg displacement until actuator limits were reached.The relationship remained independent of leg compression for displacements up to 10 cm below torque-saturation limits.
- Stiffness identification: 266 N/m: maximum measured stiffness without damping, versus 360 N/m commanded stiffness.Measured stiffness matched commands well below 150 N/m but was lower at higher desired stiffness.
- Interpretation: The force–displacement linearity demonstrates stiffness regulation without torque sensing, while friction, transmission flexibility, and motor-joint position error likely explain high-stiffness discrepancies.The external force and leg-height instrumentation provided reference measurements for evaluating the impedance controller.
2) Drop experiment:
Drop tests evaluated high-speed leg impedance, repeatability, and contact sensing under impacts. The leg showed transient oscillations and hysteresis but retained linear force behavior, while the contact sensor detected contact substantially faster than motor-current estimation.
- Drop experiment: 0.24 m: the 2-DOF leg drop produced simultaneous high torques and speeds at 150 N/m stiffness and 0.5 N s/m damping.The experiment used low damping to assess impact impedance capabilities.
- Drop experiment: 50 ms: large oscillating forces appeared during the first impact, followed by losses and a lower second peak.Steady-state leg forces settled at 6 N, corresponding to the leg, slider, and electronics weight.
- Drop experiment: Ten repeated drops showed hysteresis from friction and structural deformation, with low post-impact variance and preserved linear force–compression behavior.The hysteresis could be compensated with active control, but compensation was outside this experiment’s goal.
- Dynamic motion: 0.65 m: the leg achieved approximately twice its leg length in a jump and landed without damage.Periodic vertical joint-position control generated this dynamic motion.
- Contact sensor validation: 3 ms versus 31 ms: contact sensing delayed detection by about 3 ms, compared with motor-current estimation under a no-false-positive threshold.Lower current-estimation thresholds caused recurring false positives when leg length or impedance changed.
B. Dynamic behavior of the quadruped robot
The quadruped’s dynamic experiments use motions generated by a centroidal-dynamics kino-dynamic planner and a controller that distributes foot forces while regulating body motion. The approach includes low-impedance foot control to handle hard impacts.
- Planner and experiments: The experiments demonstrated quadruped motions computed with a centroidal dynamics-based kino-dynamic planner.The paper presents these as real-robot experiments.
- Planner and experiments: The optimizer alternates centroidal dynamics with full-body kinematics until locally optimal, dynamically consistent trajectories are obtained.The optimized variables include center of mass, momentum, contact forces, and full-body motion.
- Quadruped controller: The controller distributes foot contact forces to generate a center-of-mass wrench regulating reference CoM, angular momentum, and base orientation trajectories.It also adds low-impedance foot control for hard-impact dynamics.
1) Kino-dynamic motion optimizer and controller:
The controller uses optimized reference trajectories to regulate the robot’s center of mass, angular momentum, base orientation, and contact forces while maintaining compliant foot motion.
- Kino-dynamic motion optimizer and controller: Reference trajectories from the motion optimizer specify the desired center-of-mass wrench for the controller.The reference includes center-of-mass, angular-momentum, and base-orientation trajectories.
- Kino-dynamic motion optimizer and controller: Positive-definite gain matrices regulate center-of-mass position, angular momentum, and base orientation, including quaternion orientation errors.The quaternion error is mapped into an angular velocity vector using a logarithm mapping.
- Kino-dynamic motion optimizer and controller: Force allocation solves a quadratic program over contacting feet to produce the desired center-of-mass wrench while enforcing friction constraints.Contact activation uses both the motion plan and foot contact-sensor feedback; slack variables keep the program feasible.
- Kino-dynamic motion optimizer and controller: The resulting foot forces are converted into actuation torques using each foot’s actuated Jacobian, then combined with a low-impedance leg-length controller.The torque computation uses the vector between each foot and the base origin.
- Kino-dynamic motion optimizer and controller: The architecture supports multi-turn joints and reversible knee configurations, enabling obstacle negotiation and stand-up motions after falling onto the robot’s back.Each leg joint supports up to three turns in each direction.
3) Tracking kino-dynamic plans:
The robot tracks kino-dynamic plans across balancing, walking, jumping, and obstacle scenarios, while its mechanical and sensing choices target lightweight force-controlled locomotion under impacts.
- Tracking kino-dynamic plans: The robot follows kino-dynamic plans for balancing, slow and fast walking, and jumping without replanning during long walking motions.The reported walking plans lasted up to 15 s.
- Tracking kino-dynamic plans: The robot traverses an unmodeled seesaw obstacle and balances on moving platforms without environmental knowledge.These experiments support robustness to uncertain environments and stabilization of long motion plans.
- Tracking kino-dynamic plans: Multi-turn joints and bidirectional knee configurations let the robot reorient its legs, reach obstacles from above, and stand after falling onto its back.Figure 9 illustrates these motion sequences and configurations.
- Design choices: The design uses low-weight BLDC actuators, a 9:1 transmission, and a distally mounted touch sensor to support proprioceptive force control and hard-impact contact detection.The touch sensor is presented as a simple, inexpensive spring-loaded aperture design.
- Design choices: High peak impact torques constrain gear-train design, motivating alternatives to small single-point-contact spur gears in dynamic legged robots.The paper discusses planetary, cable, belt, and chain-driven transmission approaches in this context.
2) Impedance control capabilities:
The actuator module demonstrates strong impedance-control capability, while the open-source, lightweight architecture supports inexpensive reproduction and safe experimental use. Experiments achieved leg stiffness comparable to reported running-human values and enabled dynamic motion regulation.
- 266 N/m leg stiffness corresponds to a dimensionless leg stiffness of 10.8 in 2-DOF leg experiments.This value falls within the reported running-human range of 10 to 22.
- The measured stiffness places the robot’s capabilities within a range comparable to human leg stiffness.Reported running-human leg stiffness corresponds to dimensionless values between 10 and 22.
- The system achieved very good impedance control despite torque differences caused by gear, belt, structural-flexibility, and inertial losses.Motor torque was measured through current, while end-effector torque differed because of transmission and leg dynamics.
- The 8-DOF quadruped cost approximately 4000 e in materials and can be safely operated and transported by a single researcher.Its low weight and simplicity also simplify experimental environments.
- The controller regulates motions generated with a full-body kino-dynamic optimizer while the robot produces very dynamic motions with excellent impedance regulation.The conclusion identifies a simple torque controller for this purpose.