Bicycle balance assist system reduces roll and steering motion for young and older bicyclists during real-life safety challenges

Design and implementation of the speed-adaptive feedback controller

The dynamics of the bicycle are represented by a pair of coupled second-order differential equations (Papadopoulos, 1987): $M\left[\begin{array}{c}\hfill \ddot{\varphi }\hfill \\ \hfill \ddot{\delta }\hfill \\ \hfill \hfill \end{array}\right]+v{C}_1\left[\begin{array}{c}\hfill \dot{\varphi }\hfill \\ \hfill \dot{\delta }\hfill \\ \hfill \hfill \end{array}\right]+\left(v^2{K}_2+g{K}_0\right)\left[\begin{array}{c}\hfill \varphi \hfill \\ \hfill \delta \hfill \\ \hfill \hfill \end{array}\right]=\left[\begin{array}{c}\hfill T_{\varphi }\hfill \\ \hfill T_{\delta }\hfill \\ \hfill \hfill \end{array}\right]$where (ϕ, δ) are time-dependent quantities, representing the roll and steer angles, and (T_ϕ, T_δ) represent the applied roll and steer torques (T_ϕ, T_δ), respectively. The constant matrices M, C₁, K₀, and K₂ represent various properties of the bicycle, and v and g represents the forward speed and acceleration due to gravity, respectively. We evaluated the stability of the uncontrolled bicycle by computing the eigenvalues of the system, derived from the characteristic equation of the benchmark bicycle (Meijaard et al., 2007) illustrated in the top panel of the Fig. 1: det(Mλ² + vC₁λ + gK₀ + v²K₂) = 0. (1)${\displaystyle M=\left[\begin{array}{cc}\hfill 80.817\hfill & \hfill 2.319\hfill \\ \hfill 2.319\hfill & \hfill 0.298\hfill \end{array}\right],C_1=\left[\begin{array}{cc}\hfill 0\hfill & \hfill 33.866\hfill \\ \hfill -0.850\hfill & \hfill 1.685\hfill \end{array}\right]}$ (2)${\displaystyle K_0=\left[\begin{array}{cc}\hfill -80.95\hfill & \hfill -2.600\hfill \\ \hfill -2.600\hfill & \hfill -0.803\hfill \end{array}\right],K_2=\left[\begin{array}{cc}\hfill 0\hfill & \hfill 76.597\hfill \\ \hfill 0\hfill & \hfill 2.654\hfill \end{array}\right]}$ The real part of a complex eigenvalue, represented as a in λ = a ± bi, represents the rate of exponential decay or growth in the system’s response (this can be derived from e^at). In the interpretation of our eigenvalues graph, a positive real part implies an unstable mode and the imaginary part b gives the oscillation frequency, which is expressed as 2πf, where f is the frequency in Hz (1/s).

In the uncontrolled bicycle, the weave mode (shown with a yellow o-shaped marker line in Fig. 1) becomes unstable at low forward speeds (top left panel; 1 to 4.3 m/s), while the capsize mode (depicted with a solid blue line in Fig. 1) becomes unstable at higher forward speeds (top middle panel; 4.3 to 6  m/s). The system’s eigenvalues revealed that the uncontrolled bicycle, at forward speeds between 1 and 10 m/s, is laterally unstable, apart from a range approximately between 4.3 to 6  m/s, where it exhibits lateral self-stability (Meijaard et al., 2007).

Subsequently, the speed-adaptive feedback controller was incorporated into the model. Our control objective was to stabilize the system at all forward speeds, specifically within the linearized dynamics about an upright position, with a zero-steer angle, and a constant forward speed. Our system is represented by the linear state-space model $\dot{x}=Ax+Bu$, where $\mathbf{x}={\left[\varphi ,\delta ,\dot{\varphi },\dot{\delta }\right]}^T$ is the state vector ($\dot{\varphi }$ and $\dot{\delta }$ are representing roll rate and steering rate, respectively), and u = [T_δ] is the control input vector. The coefficient matrices A and B are given by: (3)${\displaystyle A=\left[\begin{array}{cc}\hfill 0\hfill & \hfill I\hfill \\ \hfill -M^{-1}\left(K_0+v^2{K}_2\right)\hfill & \hfill -M^{-1}v{C}_1\hfill \end{array}\right],B=\left[\begin{array}{c}\hfill 0\hfill \\ \hfill M^{-1}{\left[0,1\right]}^T\hfill \end{array}\right]}$

The control input T_δ adapts to feedback from the roll rate and roll angle, the predominance of each being dependent on the forward speed (Schwab, Kooijman & Meijaard, 2008). At speeds less than 4.7 m/s, T_δ responds only to roll rate feedback, whereas it relies more on roll angle feedback at speeds exceeding 4.7 m/s. Both types of feedback are modulated by a speed-dependent control gain.

At low speed, the control gain, K_L, is defined by the equation K_L =  − K_v(v_max − v_n), where v_n represents the current speed, v_max denotes the critical speed (this is the speed at which the bicycle transitions between two unstable regions, influenced by different modes based on eigenvalues; it can be chosen to be between 4.3 to 6 for the bicycle presented), and K_v, ranging from 6 to 14, is a constant for lower speeds. Thus, the control input is given by $u=T_{\delta }=K_L\dot{\varphi }$.

For high-speed situations, the control gain, K_H, is given by K_H =  − K_c(v_n − v_max), where K_c is a constant for higher speeds, set at 0.8 (Schwab, Kooijman & Meijaard, 2008). This formula yields the control input as T_δ = K_Hϕ.

We then manually tuned K_v and K_c to maximize stability across most of the speed range while simultaneously minimizing the required steering torque. The stability as indicated by the negative real part eigenvalues was achieved by iteratively tweaking the feedback gains. Our results demonstrated that with the implementation of this controller, the stability region of the bicycle shifted to lower forward speeds (1.3  m/s) and, at higher speeds, the bicycle motion was marginally stable compared to its uncontrolled motion (Fig. 1).

It should be noted that the model, which does not account for the rider’s relative motion to the bicycle, might yield slightly different results in comparison to real scenarios. Therefore, the controller in the bicycle has some proprietary elements that improve behavior in edge cases. To validate our findings, we conducted subjective pilot tests with riders using the chosen gains before the experiment. The resulting motion was perceived as smooth and responsive by the riders, without any signs of excessive steering, thereby validating our approach. We kept the control gain constant throughout the experiment for all participants.

Instruments

The participants rode a Gazelle step-through city electric bicycle (Arroyo C8 electric), that has been modified as a balance assist bicycle with a custom direct drive steering motor embedded in the headtube (Fig. 2). This motor is meant to provide an additional torque between the headtube and the steer tube, helping the rider in the balancing task. We instructed all participants to use the same constant gear setting while cycling. They were asked to maintain a self-selected ‘constant’ speed between 2 and 5 m/s in eco mode (the mode with the lowest propulsion assist). This approach aimed to leverage the bicycle’s instability at lower speeds. To verify that participants adhered to the speed instructions, we conducted a post-hoc ANOVA analysis (see Appendix S1, Speed).

With balance assist prototype, the bicycle’s forward speed, roll and steer angle and rate are measured or estimated. The balance assist bicycle is equipped with a wheel speed sensor on the rear wheel. Additionally, a Bosch steering angle sensor is positioned at the steering tube to measure the steering angle and steering rate. This sensor has an absolute physical resolution of 0.1 degree and operates at a sampling rate of 100 Hz. Furthermore, an inertial measurement unit (IMU) is mounted on the rear frame, allowing for accurate measurement of the roll rate and estimation of the roll angle. Additionally, it includes data acquisition and control boards located in its rear luggage rack. The steer motor applies up to 7 Nm torque between the rear frame of the bicycle and the steering tube. We evaluated the effectiveness of the balance assist system in young and old cyclists by creating a series of conditions comparable with real-life cycling challenges. To directly investigate the rider’s motion, a 3-axis IMU sensor (Shimmer Research Ltd, Dublin, Ireland) was mounted on the spine at the T7 level by an elastic strap on the back of the participant (Appendix S1, Fig. 1) prior to performing the experiment.

Participants

Thirty-two participants (18 old, 67 ± 4 years old, 174 ± 8 cm, 83 ± 14 kg, 6 females; and 14 young, 23 ± 2 years old, 179 ± 10 cm, 71 ± 12 kg, three females) participated in this study. The participants were recruited by advertisements. All participants signed a written consent form and were able to cycle and had no balance disorders or history of injury or fall caused by instability over the last year. The Human Research Ethics Committee of the Delft University of Technology (The Netherlands) approved the experiments (Letter of Approval 2080).

Experimental procedure

All participants first cycled for 2–5 min to get familiarized with the bicycle with and without the balance assist system (blind setup), and to reduce the habituation effect throughout the experiment. Then participants performed 16 trials divided in two scenarios (single- and multi-task cycling; Fig. 3).

To minimize potential biases, we employed a randomized sequence for the trials. However, we consistently scheduled single-task scenarios before multi-task scenarios. This approach was intentionally chosen to mitigate situations where an older participant might be unable to complete all trials, ensuring the collection of a complete dataset for at least one scenario. This precaution proved crucial during our study when one participant was unable to complete the full range of trials.

To maintain consistency in posture throughout all trials, participants were instructed to sit upright with both hands on the handlebars. We individually adjusted the saddle position for each participant to ensure a consistent and upright seating position.

Data analysis

We collected time series data from various sensors, including the steering angle sensor, the rear frame IMU, and the IMU placed on the rider’s torso. We analyzed the data to obtain the bicycle’s steering rate, roll rate, and rider’s upper body lean rate relative to the ground as the outcome measures (dependent variables).

To study the effect of different conditions on these dependent variables, we first extracted and segmented relevant data from the sensors, along with forward speed and yaw rate data. We manually identified the start of cycling when the forward speed increased from 0 m/s. We then divided the time series data into two phases: the transient phase when accelerating from zero to a steady-state phase where the speed was approximately constant until the end of the track. For analysis, we used the steady-state phase of the time series data as a segment of interest (Appendix S1, Fig. 3).

To determine the start indices for each segment of interest, we used the first index at which forward speed reached 1.5 m/s in the accelerating phase. To determine the end indices for each segment of interest, we used two criteria: the first index at which either forward speed reached 1.5 m/s in the decelerating phase or the absolute difference in yaw rate was greater than or equal to 4, indicating a change in cycling direction at the end of the cycling track. We chose 4 deg/s yaw rate as a threshold for starting to turn after visually inspecting all trials.

We updated the start and end time points to segment all signals from the bicycle’s and rider’s IMUs and the steering angle sensors. To reduce high-frequency noise in the signals, we applied a low-pass second-order Butterworth filter with a cutoff frequency of 25 Hz on the roll rate and steering rate signals. We also detrended those resulting filtered signals by subtracting their mean values.

We then calculated the mean absolute steering rate, roll rate, and lean rate of the time-series data over each segment that represented an approximate steady-state traversal. Finally, we calculated the average of two repetitions per condition to reduce the effect of randomness in balance control.

Note that, desirably, we wanted two repetitions per condition. However, in a few cases, due to malfunctions, the system did not apply the perturbation, resulting in trials being labeled as not disturbed. For the analysis, we reported the average of the maximum number of repetitions per condition. If subjects had no trials performed for a particular condition, we excluded them from the analysis. For illustration purposes, we included representative time series of bicycle motion data of all conditions in single-task scenario in Fig. 4.

Statistics

To evaluate the effects of the Balance Assist System, Disturbances, and Aging on dependent variables (steering, roll, and rider’s lean rate), we performed repeated measures ANOVA with Balance Assist System (on/off) and Disturbances (on/off) as within-subject factors and Aging as a between-subjects factor. In the case of a significant main effect, we investigated the interactions of effects, and if significant, post-hoc ANOVA was performed to test the effect of Balance Assist System on affected variables.

To evaluate the effects of Scenarios (multi-tasking) we performed the repeated measures ANOVA on dependent variables with Balance Assist System (on/off) and Scenarios (single-task/multi-task) as within-subjects, and Aging as a between-subjects factors on Undisturbed trials. Since the duration of disturbances was different in single- and multi-task cycling, to evaluate the effect of Scenarios, the disturbed trials were excluded for a fair comparison between two scenarios.

Finally, in case of effectiveness of the balance assist system in improving the outcome measures, to gain insights into how the balance assist system affects each age group separately, we conducted a simple main effects analysis. We divided the data by age group and performed an ANOVA on each group to examine the effect of the balance assist system on the roll rate and steering rate.

We performed the statistical analysis in JASP (University of Amsterdam, The Netherlands) version 0.16, and p < 0.05 was considered significant.

Effects of balance assist system, disturbances, and age per scenario

Effects of the balance assist system, disturbances, and age in multi-task cycling

In multi-task cycling, there was no significant effect of Aging on steering rate (Fig. 6, Table 2). However, there were effects of Balance Assist System and Disturbances on steering rate. While steering rate was higher in disturbed compared to undisturbed cycling (t = 10.566, p < 0.001, Cohen’s d = 1.997), activation of the Balance Assist System, regardless of age or disturbances, significantly reduced steering rates compared to deactivation (t =  − 3.249, p = 0.003, Cohen’s d =  − 0.614).

The analysis of roll rate in multi-task cycling revealed significant strong effects of Disturbances and the Balance Assist System on bicycle roll rate with no significant effects of Age or any interactions between the main factors (Fig. 6, Table 2). Post-hoc analysis showed higher bicycle roll rates in disturbed compared to undisturbed cycling (t = 7.771, p < 0.001, Cohen’s d = 1.469). Activation of the Balance Assist System resulted in significantly lower bicycle roll rates, regardless of age or disturbances (t =  − 4.623, p < 0.001, Cohen’s d =  − 0.874).

In multi-task cycling, neither Age, Disturbances, nor the Balance Assist System had a significant effect on riders’ lean rate (Table 2).

Effects of balance assist system, scenarios, and age (undisturbed cycling)

There was no significant effect of Aging on the bicycle’s steering rate. However, significant effects were observed for both Scenario and the Balance Assist System on the bicycle’s steering rate (Table 3), without any interactions between these main factors. Post-hoc analysis showed that the steering rate during multi-task cycling was significantly higher than during single-task cycling (t = 4.436, p < 0.001, Cohen’s d =  − 0.838. Additionally, activation of the balance assist system led to a decreased steering rate, irrespective of whether the cyclist was engaged in single- or multi-task cycling scenarios (t =  − 5.889, p < 0.001, Cohen’s d =  − 1.113).

Furthermore, there were significant effects of Aging, Scenario, and the Balance Assist System on the bicycle’s roll rate (Table 3). Post-hoc analysis showed that the roll rate was higher in older adults compared to young adults (t = 2.586, p = 0.016, Cohen’s d = 0.489), and higher during multi-task scenarios compared to single-task scenarios (t = 3.747, p < 0.001, Cohen’s d = 0.708). Regardless of Age and Scenario, the bicycle’s roll rate was lower when the balance assist system was activated, compared to when it was deactivated (t =  − 6.187, p < 0.001, Cohen’s d =  − 1.169).

There was not any effect of Aging, Scenario, or Balance Assist System on rider’s lean rate (Table 3).

Balance assist system and aging

Our study found a significant effect of aging on roll rate and a trend towards higher steering rates among older participants, indicating reduced ability to control the bicycle’s rolling motion and suggesting that age may impact bicycle balance control. Regardless of age, our results showed improved bicycle balance control when the balance assist system was activated.

Recent research suggests that aging impacts the brain’s capacity for processing sensory inputs into motor actions (Moulton, Rudie & Dukelow, 2022), and our findings suggest that the balance assist system may assist older cyclists by processing the bicycle’s states earlier than would occur in their central nervous system. This leads to a faster control action to damp lateral motion in the ‘older rider-bicycle’ system when the balance assist system is activated. Simple main effect tests showed that the balance assist system reduced roll rate in both single-task and multi-task cycling, with a greater effect on older cyclists’ roll rate (single-task; Older: F = 51.547, p < 0.001, η² = 0.752, Young: F = 10.386, p = 0.007, η² = 0.444 and multi-task; Older: F = 14.113, p = 0.002, η² = 0.502, Young: F = 8.355, p = 0.014, η² = 0.410). Furthermore, e-bikes reduce the physical effort for propulsion, but do not provide fatigue reduction in the steering and balancing task. While steering in the long term may lead to fatigue and increase the risk of falling, especially in older cyclists (Weavil et al., 2018), the decreased steering rate using a balance assist system is promising to possibly reduce the fall risk. The balance assist system assisted older adults more than young in reducing their steering rate in single-task (single-task; Older: F = 44.759,  p < 0.001, η² = 0.116, Young: F = 8.675, p = 0.011, η² = 0.076), and all undisturbed trials among both scenarios (Older: F = 42.335,  p < 0.001, η² = 0.751; Young: F = 9.226, p = 0.01, η² = 0.435).

The increased number of single-actor bicycle crashes due inadequate balance control, especially in older cyclists, suggests that our system could induce balance control closer to young cyclists, potentially leading to safer cycling and reduce the number of age-related accidents. However, future research with larger sample sizes, various maneuvers, and a longer duration of cycling may be needed to confirm this trend and determine its significance.

Balance assist system and cyclists’ lateral balance control; lean rate

We did not observe any effect on the rider’s lean rate with respect to the ground. This might be due to the rider’s natural tendency not to lean when they can also steer to maintain the bicycle’s balance, aligning with optimal control predictions (Sharp, 2008).

Additionally, prior observations (Kooijman, Schwab & Moore, 2009; Moore, Kooijman & Schwab, 2011) provide evidence that riders tend to keep their upper body relatively inertially stationary during straight riding, even if the bicycle’s roll motion has relatively larger variability. In essence, it seems easier for riders to allow the low inertia bicycle to roll than to move their bodies along with it for control purposes. This could explain the lack of lean rate changes we observe in this study.

Alternatively, ineffectiveness of the balance assist system on the lean rate (torso lateral motion) could be explained by the fact that the balance assist controller does not measure or estimate the rider’s state. While the controller succeeded in keeping the bicycle in an upright position with less lateral oscillation in presence of the balance assist system, it is not clear whether the riders were able to accept the control action induced by the steering motor without over-reacting. Therefore, further investigation is necessary to understand the rider’s perception and intention.

Limitations and suggestions

There are some limitations in our study to note. We collected the older participants’ data at a parking lot at the Den Haag Gazelle User Experience Center and the young participants at a parking lot at TU Delft with slightly different road surfaces (asphalt vs. cycling path bricks). However, by ensuring that all data per participant was collected consistently within the same environment, we mitigated the risk of skewed results.

The core findings of our study regarding the effectiveness of the balance assist system were drawn from the within-subject changes in variables (variables activated - variables deactivated). Therefore, these conclusions can be considered largely independent of the test location. However, it is crucial to note that the impact of aging on bicycle balance control may not be entirely independent of the test location. Factors such as differences in road surfaces may influence these findings. Therefore, future research could look into controlling these variables more effectively to fully comprehend the relationship between age and bicycle balance control.

Moreover, in human–robot interactions, ‘trust’ is seen as a key to improve the operations and a feeling of safety (Goillau, 2003). Therefore, it is expected that when adapting to new assistive technologies, the positive effect of the assistive system is more pronounced when riders trust the technology and yield to the generated steering torque by the steering motor. Since there is no direct measurement of the rider’s effort, again we cannot draw a strong conclusion whether that was by choice or the rider’s put enough effort in optimizing the lateral motion variability. However, we have asked riders to perform trials in a consistent manner; therefore variation in effort is not expected per participant, and the results are more likely due to the action of the balance assist system rather than changes in the riders’ action.

We observed that five out of 18 older adults (all males) failed at least once in performing the first multi-task trial. It might be interesting to study the effect of gender on multi-task cycling to address adequate regulations for older male cyclists. In future studies, we recommend estimating the lateral position of the bicycle and calculating the deviation of the rider-bicycle from the straight-line, especially during multi-task cycling.

One of the common issues among our older participants was having a stiff neck, which would not allow them to look over the shoulder without using their torso. The problem with that is a higher variation of motion while their range of motion is limited compared to young participants and that influences their motion coordination and lateral balance. A small side mirror added to older participants’ bicycles could potentially help to eliminate some of the hazards, but careful adaptation is necessary to accurately identify the direction and distance of motion of other objects through the mirror.