Crash test-based assessment of injury risks for adults and children when colliding with personal mobility devices and service robots

Autonomous mobility devices such as transport, cleaning, and delivery robots, hold a massive economic and social benefit. However, their deployment should not endanger bystanders, particularly vulnerable populations such as children and older adults who are inherently smaller and fragile. This study compared the risks faced by different pedestrian categories and determined risks through crash testing involving a service robot hitting an adult and a child dummy. Results of collisions at 3.1 m/s (11.1 km/h/6.9 mph) showed risks of serious head (14%), neck (20%), and chest (50%) injuries in children, and tibia fracture (33%) in adults. Furthermore, secondary impact analysis resulted in both populations at risk of severe head injuries, namely, from falling to the ground. Our data and simulations show mitigation strategies for reducing impact injury risks below 5% by either lowering the differential speed at impact below 1.5 m/s (5.4 km/h/3.3 mph) or through the usage of absorbent materials. The results presented herein may influence the design of controllers, sensing awareness, and assessment methods for robots and small vehicles standardization, as well as, policymaking and regulations for the speed, design, and usage of these devices in populated areas.

where ||ẍ H || 2 represents the norm 2 resultant head acceleration at a given time interval ∆t below 15ms. Injury reference injury values for non-blunt impacts on these two metrics were originally set to a HIC15 of 790 and 1000 for a 20% and 50 % probability of serious injury p(AIS3+) 2 . Whereas, the cumulative acceleration a 3ms injury reference value for the Q3 dummy is 81 and 99 g for a 20% and 50% probability of injury, respectively. However, what would deem as a correct set of injury criteria for children is yet a research question. Recently, a few studies have focused on understanding the biomechanical constitution of children and subsequent injury risks of each body part such as head injury in young children 1,3 which showed that head injuries for peak skull stress in 3-YO models correlated to a HIC of 543. This goes in line with the most recent EuroNcap update where the reference value for 5% of p(AIS3+) and p(AIS4+) was set to a HIC15 of 500.
As the most conservative approach an estimated p(AIS3+) as a function of HIC15 was used based on regression function from Ref. 4 , as follows: where the constants for α = 3.39, β = 200, γ = 0.00372 were fitted to a logistic regression of injury data in Ref. 5 . The scaling factor for a child dummy Q3 was λ HIC = 0.71 2 .
In comparison, adult injury reference values are HIC15 of 700 and 1000 for a 5% and 20% p(AIS3+) respectively 6 . Currently, the EuroNcap 7 set capping acceptable limit to the 5% value (700) for passenger protection.

Chest Injury Criteria
Several metrics can be used to assess the probability of injury at the chest. The most notable and widely accepted viscous criteria for soft tissue criteria for car crashes has not been validated for children for lack of data. Therefore, the criteria used in this evaluation was the chest deflection CD = ||∆x C || 2 , where ||x|| 2 denotes the Euclidean norm over the chest, which is directly related to the probability of rib fractures. According to the IARV from the EEVC 2 ), a deflection of 33 and 46 mm causes a 20% and 50% probability of serious injury, respectively. Nevertheless, this threshold was obtained for shoulder belt restraining systems and can thus be considered a more conservative and realistic comparison to using the airbag blunt impact values for the probability of serious thoracic injury p(AIS3+) from the National Highway Traffic Safety Administration (NHTSA) vehicle assessments 8 using the conversion factors for airbag (λ CD = 0.44) provided by the EU CHILD project 2,9 p (AIS3+) = 1

Neck Injury Criteria
The injury probability used to determine the AIS level for the neck was the maximum value out of three metrics: the maximum extension forces (F z ), the maximum shearing forces (F x ), and the maximum extension moments (M y ). This study used reference values from the EuroNCAP 10 and EEVC 2 , where the 20% probability of AIS3+ is N z = 1.55kN, or My = 79Nm, whereas the 50% probability of AIS3+ is N z = 1.705kN, or My = 96Nm. Additionally, we used the cumulative exceedance forces to assess the prolonged exposure to a tension force during extension moment 10 .

Tibia Injury Criteria
For the analysis of adult pedestrians, three metrics were used for comparison with known thresholds in different studies: 1) The TI index used in automotive crash test assessments [EuroNCAP 7 and NHTSA 8 ] is given by: T I = F z /F zc + M R M Rc , with F z the measured tibia proximal force in kN and F zc = 35.9kN a normalized reference value. M R represents the resultant torque in [Nm] for the knee M x , M y as M R = ||M x , M y || 2 , while M Rc = 225Nm is the normalized reference value for the adult dummy H3. The IARV detailed in Ref. 6 is set to 5% of pAIS2+ for T I = 0.4 and 20% of pAIS2+ for T I = 1.3. Second, the revised tibia index (RTI) 11 was used to determine the probability of incurring injuries at AIS2+ injury level (moderate injury) in adults. This index applies to lower extremity impacts, including impacts at the lower and upper tibia, and resulting torques at the knees, ankle, and foot. The associated probability o AIS2+ injury is computed as follows: RTI is computed as the TI index but using the following reference values: M Rc = 240Nm, and F zc = 12kN, see 11 . Third, the probability of tibia fracture was determined using the compression axial force criteria TCFC. This last metric was recently developed as a Weibull distribution to determine lower limbs injury risk per age and gender 12 , accounting for differences and variability in bone density over the life span. This complements metrics valid for 35-year-old adult male and used traditionally 8,13 ]. where the risk function Ramg for age, mass, and gender is defined as: where constants k 0 − k 3 were defined for male and female in the groups below 40 and above 40-years-old independently in Ref. 12 .
A limitation in this last metric from Ref. 12 is that the probability of tibia bone fracture was set from a single predictor based on the axial compression force. Thus, it can only provide partial results and serve mostly to compare different effects for more vulnerable populations, such as elderly adults and lighter people.

Head model simulation values
The model of the head impact was used for comparing different materials (see, Supplementary Table S4), at contact speeds ranging 0.5 to 7.0 m/s , and impacting masses ranging from 10 to 200 kg. Moreover, we evaluated the overall effective stiffness k hr assuming constant properties in the skull and varying linearly the effective stiffness, which could result from structural arrangements in the robot (see Supplementary Fig. S2). Each variable in the model was evaluated independently using other parameters from real experimental data. In Fig. 6A, the head properties were assessed for children aged 3-4-YO, 6-7-YO, and 10-12-YO 3, 14, 15 with masses of 2.7, 3.4, and 3.7 kg. The head radius r h used were 0.056, 0.078, and 0.08 m, respectively. The elastic modulus E h were 4.7, 5.7, and 6.0 GPa respectively. The Poisson ratio ν h were 0.26, 0.24, and 0.23 respectively. For comparison with an adult head, we simulated using a mass of 4.54 kg, Elastic modulus of 6.5 GPa, and a Poisson ratio of 0.22 16 .

Service robot categories:
A wealth of service robots and other small personal mobility devices have appeared on the market worldwide. It would be impossible to cover them all. Figure 1 compares a selected subset of existing mobile service robots (MSR) and personal mobility devices (PMD) that share the ground with pedestrians today in different regions of the world. We compare pedestrians and MSR/PMD in terms of their respective speed (and speed limits), height and weight. Figure 1A, speed limits for powered PMDs usage in pedestrian lanes in the US 17 , Japan 18 , the UK 19 , and EU 20 . Speed limits for scooters, and PMDs in the US 17 , UK 21 , Japan 22 , Australia 23 , and the EU 20 . Figure 1B, Average walking speed of pedestrians aged 12 to 70 years old 24 and children <2 years old obtained from Ref. 25 . Figure 1C

Risk of injuries in child pedestrians
Further analysis for less severe injuries to the head could be derived from the peak resultant accelerations, which showed low values of 30 and 62 g for the two lower speeds, respectively. Meanwhile, a peak acceleration of 194 g was noted at 3.1 m/s (11.1 km/h / 6.9 mph) (see Supplementary Fig. S3), which exceeded the known concussion threshold of 62.4 ± 29 g for young people 33 )and the 5% skull fracture probability (180 g) -also a metric of p(AIS3+) 5 .
Injuries to the neck as a second important metric for head impacts (Fig.2C) were analyzed by the cumulative tension forces under extension bending moments and compared with limits for serious injuries (pAIS3+) scaled for Q3 child dummies 9, 34 ). Shear forces in the neck showed no significant associated indices of injury. Time-series data is available in Supplementary Figure S3 C-D.

Lower leg injuries
For the child dummy, the impact force resulted from the blunt unconstrained lateral collision at the tibia (see Supplementary  Fig. S5) . In the current standards and normative data for crash testing, child dummies lack measurement equipment at the lower body; therefore, we measured from the robot's force cell in the reaction forces and compared them with responses in adults. Results show that impact forces of 2.19 kN, 0.86 kN, and 0.33 kN, respectively, are incurred at 3.1m/s, 1.5m/s, and 1 m/s, respectively. In this case, we selected a lateral collision with a pedestrian on the double stance phase of the walking gate cycle, which would be the worst-case scenario for a direct blunt impact given that the weight is evenly distributed in both legs. There is no documented way to relate directly these values to a probability of injury in children. Nevertheless, these data can be compared to injury criteria applied to adults: for instance, impact forces ≥ 1.4 kN yield a 14.9% probability of moderated injury (AIS2+), such as tibial fractures. Detailed data in Supplementary Table S2. On the adult dummy, our results showed that regardless of the speed, all impacts displayed a TI > 0.4 on the impacted leg (right). This reference injury value exceeded the 5% probability of fracture at the tibia, which was considered a moderate injury (AIS2+). The TI values were 1.16, 0.73, and 0.53 at speeds of 3.1, 1.5 and 1.0 m/s, respectively (Fig. 4B). All values were within the acceptable threshold for passenger vehicles (TI < 1.3) used in vehicle crash testing at a 20% probability of injury. The corresponding peak forces on the robot's impactor (Fig. 4C) reached 4.4 1.4, and 0.84 kN, at speeds of 3.0, 1.5, and 1.0 m/s, respectively. Other injury metrics are available in Supplementary Table S3. A second injury risk was found on the indirectly impacted leg (left leg). In this case, only at a speed of 3.1 m/s (11.1 km/h / 6.9 mph). Two indicators showed the same risk level: TCFC of 3.89 kN and a TI value of 0.81. Detailed time-series data are available in the supplementary material for both legs (see Supplementary Fig. S7-S9).
Finally, we used a new metric proposed in Ref. 12 ) for lower-limb injury risk, although limited to a single predictor from the internal force compression it accounts for age and gender. The probabilities of fracture from internal compression force alone were 1.9% for men and 3.2% for women under 40 at a speed of 3.1 m/s (11.1 km/h / 6.9 mph); whereas pedestrians over 70 years old would have a risk probability of 3.1% and 5.5% for men and women, respectively.

Injuries from secondary ground impact
All impact conditions caused the dummies to fall due to the sufficiently high impact energy of the robot to destabilize the standing pedestrian dummies. Detailed data is available in Supplementary Table S4.
After comparing head injury severity between child and adult pedestrians, we noted (see Fig. 5A) that only one out of three trials in which the adult fell would have caused a serious head injury [p(AIS3+) > 50%], whereas 7 out of 14 trials in which the child fell would have caused a serious injury [p(AIS3+) > 50%]. Moreover, 4 out the 14 trails caused p(AIS3+) > 20%, whereas 2 out the 14 trails caused p(AIS3+) > 5%. No significant head injury probability [p(AIS3+) < 5%] was observed in only 1 out of the 14 trials. Moreover, three tests resulted in a HIC > 6000 (AIS4+ > 98% -critical or life-threatening). These impacts occurred at the thorax where the child dummy was projected forward at the highest velocity transfer.
Overall, impacts above the COM of the dummy (chest or head impacts) showed moderate to high risk of injury, with those closest to the COM resulting in higher head velocities at ground impact. However, impacts below the COM (lower legs) and beyond 1.5 m/s (5.4 km/h / 3.3 mph) produced wrap projections impacting the robot's body continuously before the forward projection to the ground, thereby decreasing the final velocity of the body when coming into contact with the ground. Videos of all impacts are provided as supplementary materials.

Evaluation of design and operational conditions
Operational velocity differences in skull changes were found when varying the impacted pedestrian (Fig. 6A)  The effect of the material's mechanical properties was evaluated by modulating the stiffness, Young's modulus of elasticity, comparing common shell/bumper plastics used by vehicle manufacturers as detailed in Supplementary Table S5.
Velocity at impact was found proportional to an increased injury rating (see Fig. 6A-B), the 5% risk of skull fracture was exceeded at 1.  (Fig. 6B), which reached 94% ± 0.14% of the peak acceleration of 200 kg impacting mass at all simulated velocities. The HIC15 index showed serious injuries p(AIS3+) from an operational speed of 1.6 m/s (5.7 km/h / 3.5 mph) for a mass of 60kg, with less than 5% ± 0.01% difference to the HIC at 200kg. Operational speeds exceeding 2.24 m/s (8.0 km/h / 5.0 mph) caused a 50% probability of serious injury based on the HIC15 (HIC15 > 1000).

4/24
Supplementary Tables   Supplementary Table S1. Representative commercially available mobile service robots and personal mobility devices. Photos' sources: Starship 35

21/24
Supplementary Video Captions: Mobile service robots and personal mobility devices can now operate autonomously around pedestrians, at speed of 3.7 up to 18 mph, with masses ranging from 20 kg to 300kg. However, these devices are not standardised, and regulations differ per country and even within single countries. We investigated the influence of operational speed and mass of a robot during impact with pedestrians, and contrasted risks faced by two different categories: children and adults.
We measured injuries to the head on blunt impacts at three speeds with an 133kg mobility device: At 3.1 m/s -accounting for the differential speed between a child running at 1.5 m/s colliding against a robot at 1.6 m/s. Head injury indicators showed a 14 % probability of a serious injury. In contrast, at the reduced impact speeds of 1.5 m/s and 1.0 m/s, all injury metrics were below the 5% risk threshold.
Chest impacts with the child dummy were recorded at the same 3 speeds of 3.1, 1.5 and 1.0 m/s. As a highly instrumented body-part on the child dummy, we recorded the same impacts with a lighter robot of 60kg, representing smaller delivery robots.
We found a significant risk of serious injury with the chest deflection criteria, reaching up to 50 % probability of a serious injury for the 133kg robot impact compared to 32 % for the 60kg robot. At lower speeds of 1.5 and 1.0 m/s, no significant injuries were found.
The final tests were performed at the lower legs of children and adults. Results showed that all impacts, regardless of the speed, displayed a tibia index exceeding a 5% probability of tibia fracture. In this injury index, we found an increased probability of tibia fracture proportional to the speed at contact: 7.7 %, 14.9% and 33.2 % at the speeds of 1.0, 1.5 and 3.1 m/s respectively.
Although child injuries to lower-legs is not yet well documented, our data displayed up to 2.19 kN of impact force at 3.1 m/s. This is a force level comparative to the adult dummy, where impact forces over 1.4 kN showed over 15% probability of lower leg injury.
We found post-impact secondary injuries due to a fall to pose a significant risk of severe injuries to head and neck. With levels of injury higher than blunt impacts alone.
Contrasting head injury severity for the adult and child pedestrians, only one out of three trials in which the adult fell would have led to a serious head injury whereas for the child falls, 7 out of 14 lead to a serious injury.
Our results show a need to regulate robots and mobility devices through operational speed or by limit their usage in densely populated areas. This set of data and their analysis may also guide the design of robot controllers, and its navigation decision-making systems for mitigate risks of impact.
This opens a path for physically safe operations of autonomous robots in public environments through standards, traffic management, and legislation.