Towards Standardized Disturbance Rejection Testing of Legged Robot Locomotion with Linear Impactor: A Preliminary Study, Observations, and Implications

TL;DR

This work addresses the absence of standardized disturbance testing for legged robot locomotion by introducing a linear pneumatic impactor as a repeatable, adaptive disturbance source. The authors formulate a discrete-time disturbance-rejection framework, distinguishing internal control from environmental disturbances, and demonstrate the approach with a Digit humanoid across three locomotion controllers in a walking-in-place task. A key finding is that disturbance tolerance can be meaningfully assessed via impact momentum, with the best controller sustaining $26.376\,\mathrm{kg\cdot m/s}$—comparable to the human benchmark of $26.506\,\mathrm{kg\cdot m/s}$—and that higher impact levels do not always predict worse outcomes, highlighting the role of controller dynamics and impact duration. This preliminary study lays the groundwork for standardized safety testing infrastructure in legged robotics, enabling fair, repeatable, and hardware-agnostic benchmarking with potential implications for certification and industrial adoption.

Abstract

Dynamic locomotion in legged robots is close to industrial collaboration, but a lack of standardized testing obstructs commercialization. The issues are not merely political, theoretical, or algorithmic but also physical, indicating limited studies and comprehension regarding standard testing infrastructure and equipment. For decades, the approaches we have been testing legged robots were rarely standardizable with hand-pushing, foot-kicking, rope-dragging, stick-poking, and ball-swinging. This paper aims to bridge the gap by proposing the use of the linear impactor, a well-established tool in other standardized testing disciplines, to serve as an adaptive, repeatable, and fair disturbance rejection testing equipment for legged robots. A pneumatic linear impactor is also adopted for the case study involving the humanoid robot Digit. Three locomotion controllers are examined, including a commercial one, using a walking-in-place task against frontal impacts. The statistically best controller was able to withstand the impact momentum (26.376 kg$\cdot$m/s) on par with a reported average effective momentum from straight punches by Olympic boxers (26.506 kg$\cdot$m/s). Moreover, the case study highlights other anti-intuitive observations, demonstrations, and implications that, to the best of the authors' knowledge, are first-of-its-kind revealed in real-world testing of legged robots.

Figures (7)

• Figure 1: The linear pneumatic impactor has been used as a standard testing equipment related to the research in automobile safety and injury biomechanics simulating impact energy to head, tibia, thorax, abdomen, and shoulder impacts: A shows the test of dummy thorax impact, B is coming from the study of head and hockey helmet instrumentation evaluation allison2015measurement, both tests were performed with the linear pneumatic impactor with different impact energies shown in C. The same device is also configured with minor modifications for legged robot locomotion testing performed in this study.
• Figure 2: The pneumatic impactor adopted in this study demonstrates its repeatability by empirically showing a linear relation between the testing action $\mathbf{u}_e$, the peak velocity achieved by the impactor, and the operator control $\mathbf{a}$, the configured pressure for the compressed air. The linear fitting error is within 0.1 m/s.
• Figure 3: The testing configuration in-lab and the conceptual illustration before and after the impact: "A" denotes the impactor face with a rectangular surface, "B" denotes the displacement potentio-meter, one can also refer to Fig. \ref{['fig:impactor_example']}C for another view of the same equipment.
• Figure 4: An overview of all 36 impact tests against three locomotion controllers: different impact phases are differentiated by the marker color and the label is specified in the form of stance foot phase (whether the left or the right foot is on the ground) and swing foot phase (whether the swing foot is going up or stepping down) with an underscore "_" in between. Note the dual support phase (with both feet on-ground) is specified as "Dual_None". The fallover status is characterized by the size of the marker. The three different locomotion controllers are differentiated by the marker type.
• Figure 5: The velocity profiles of the impactor within 0.05-second after the moment of impact.