1. Introduction
Humans and animals make use of so-called ‘preflexes’ and reflexes that modulate effective leg stiffness to manage impacts [
1,
2,
3,
4,
5]. Despite this, stiffness control in robot legs has not been directly investigated in drop landings within literature. From a biological perspective, modulation of leg stiffness generally precedes disturbances to terrain elevation [
6,
7,
8,
9] in order to mitigate injuries to the musculoskeletal system. Other circumstances, such as a variation in terrain stiffness, may also be compensated for through similar modulation [
10,
11,
12]. Focusing on the mechanism for impact compensation during drops or jumping in place, studies on humans have been reported for several decades [
3,
13,
14,
15,
16,
17,
18,
19,
20], with experimental drop heights of up to 1.93 m [
13]. While different mechanisms have been attributed to impact force attenuation during drop jumps or drop landings [
16], decreasing effective leg stiffness during an impact has been shown to reduce peak forces [
14,
15].
For mechanical shock absorption systems in applications such as motor vehicles or helicopter landing gear, magnetorheological (MR) materials have been explored widely as potential solutions to shock-induced vibration and impact loads [
21,
22,
23,
24]. In various real-world scenarios, stiffness control using MR materials, particularly MR fluid (MRF) could help mitigate costly damages to sensory equipment or prevent complete robot failure. Successful recovery from trivial missteps or more substantial drops within rugged terrain could be the difference between a successful mission and a failed task for a robot. Although it is clear that the actuators of a robot can benefit from passive and variable series elasticity in terms of impact management, efficiency, and general robustness [
25,
26,
27,
28], impact loading of robot legs with variable stiffness has not yet been reported. Hence, the extent to which MRF-based leg stiffness control can benefit legged robot shock absorption was studied herein.
In this paper, the MRF-based variable stiffness actuator leg mark II (MRVSAL-II) was evaluated through impact loading scenarios, focusing on the potential for variable stiffness in a robot leg to improve shock absorption. First, a drop-test impact-loading system was constructed to conduct impact loading experiments. Employing this system, passive performance evaluation was conducted by comparing the MRVSAL-II performance with a comparable rigid leg with relatively high stiffness and damping and a soft leg with relatively low stiffness and damping. Based on experimental performance, an adaptive impact-buffering controller was developed for the MRVSAL-II, which was investigated for its impact mitigation capability.
Following on from the introduction, this paper is organised as follows.
Section 2 outlines the functionality of the MRVSAL-II.
Section 3 details the experimental impact system.
Section 4 outlines the experimental procedure.
Section 5 presents the passive impact results.
Section 6. introduces an impact force controller and presents the controlled impact results.
Section 7 draws conclusions from the study.
3. Experimental Setup
To conduct the impact loading experiments of the MRVSAL-II, the drop-test system illustrated in
Figure 2 was developed. This system makes use of a rigid frame with four parallel 20 mm rails of 1.2 m length. Given the dimensions of the system and leg, a maximum drop height
of 600 mm can be set between the foot pad of the leg and impact platform. Two of these rails guide the falling platform to which the leg is rigidly affixed. The platform includes a removable 1.95 kg payload mass, which combines with the platform mass and leg mass to provide adjustable total falling masses
of 2.65 kg and 4.6 kg for the single leg. To set the drop height of the leg, an electric winch (XBULL3000LBS, X-Bull) is controlled to reach a desired vertical displacement using a laser displacement sensor with 800 mm range (IL-600/IL-1000, Keyence). This laser also serves to measure the displacement
of the falling platform through the impact, which has an initial value or datum position of 220 mm at the moment of impact, as illustrated in
Figure 3a. The drop height
is therefore taken as the elevation from the datum position of the leg. A servomotor-controlled release mechanism then allows the falling platform to be dropped upon command. After a certain level of leg deflection, the pivot point between the upper and lower leg segments will also collide with the impact platform, with a maximum leg stroke of approximately 123 mm, illustrated in
Figure 3a as
. To facilitate leg deflection in the sagittal plane, a low-inertia linear rail platform is located directly below the foot pad of the leg. This rail is supported by two S-type load cells (MT501-100 kg, Millennium Mechatronics), from which the measurements can be summed to provide the resulting impact force. This is illustrated between
Figure 3a,b, where it is shown that irrespective of the position of the leg through the deflection, the impact force is always
, where
and
are the forces measured by the two load cells. The included rotary MR damper within the MRVSAL-II is powered with an amplified control signal from the system controller (myRIO-1900, National Instruments), which additionally acts as the DAQ for data logging.
5. Passive Control
Included in
Figure 4a–f are the COM vertical displacements
of the MRVSAL-II during the passive impact tests with the 2.65 kg total mass as drop height
which was increased from 100 mm to 600 mm. Additionally indicated in each plot is the COM displacement which corresponds to the leg stroking out, approximately 97 mm, i.e.,
. When the COM displacement reached this threshold, a collision occurred following the initial landing of the leg’s foot pad and impact platform, influencing the dynamic behaviour of the leg during the impact. It should be noted that this did not occur for all tests and could be observed where
.
From
Figure 4a, what is initially apparent is that for the no damper case, the deflection range for the leg is the largest, accompanied by the greatest settling time of 0.47 s. On the other hand, the rigid leg behaved quite differently, even entering ballistic flight as the leg bounced upon impact. Despite this, the rigid leg settled very quickly, within 0.15 s. In between these two extreme scenarios was where we found the passive damper control modes. On a scale comparable to the extreme scenarios, not much variation between currents was observable; however, it was noticeable that at 0 A the leg deflected more and had a lower rebound than that of the 3 A case, which rose 5.90% higher. As drop height was increased, these trends became more apparent, as observed in
Figure 4b. For greater drop heights, i.e.,
Figure 4c–f, it appeared that the no damper case resulted in collision with the ground due to what appears to be a combined effect of relatively low stiffness and low damping ratio. This is quite reasonable, given the removed rotary MR damper which governs the stiffness adjustment and contributes quite high damping to the system. Despite the high impact energy for the 600 mm drop height, as seen in
Figure 4f, no passive control mode resulted in collision, although, the 0 A case was not far from it.
When the total falling mass was increased to 4.60 kg, the COM displacements for all tests became more violent, indicated in
Figure 5, given the impact energy nearly doubled for these cases. It is seen in
Figure 5a that even for a 100 mm drop height, the no damper case resulted in collision. There was also more substantial variation between the passive control modes, where it is seen that the 3 A case resulted in a rebound that was 40.1% greater than that of the 0 A case. At the 200 mm drop height of
Figure 5b, the passive control modes approached the collision threshold, with the 0 A case very narrowly avoiding collision. At this stage, it became challenging to distinguish the collision scenarios, however, so this is discussed shortly with respect to the measured impact forces. Although, what did occur here was a transition during the 300 mm impact shown in
Figure 5c, where some of the passive control modes experienced collision, but others avoided it by a small margin. In all tests following this, i.e., those shown in
Figure 5d–f, all modes except for the rigid leg resulted in collision as the leg deflected to its maximum range.
In terms of the rate at which the impact energy is dissipated, the settling time
for the COM displacement was investigated, as plotted in
Figure 6. This is indicative of the rate of energy dissipation, with the vertical kinetic energy
being a function of the COM vertical velocity
. Starting with the fastest settling times, these were generally found for the rigid leg case, indicating this scenario resulted in the greatest effective damping coefficient during impacts for a given mass. This can be explained by a few contributing mechanisms which were specific to the tests with the rigid leg. First, for every single test, the leg COM later exceeded the impact initial height of 220 mm. This is consistent with the bouncing behaviour observed during tests. As a consequence, more work was performed by the rubber foot pad attached to the leg in dissipating energy. This was further exaggerated by the relatively high stiffness of the leg, leading to greater compression of the foot pad than in other tests. It is also likely that there was greater flexure in the 3D-printed leg structure, causing greater internal energy dissipation. In great contrast, the no damper case led to the anticipated lowest effective damping coefficient, as indicated by the high settling times for these tests. For a legged robot, this would result in high vibration of the platform, which could lead to more collisions and erratic behaviour. As a reasonable middle ground, the settling times and hence energy dissipation rate of the passive controlled cases generally exist between the no damper and rigid cases. The tendency was for the 0 A cases to result in lower settling times, but as current increased towards 3 A, settling time increased. What this shows is that the effective damping coefficient for the leg during impacts is inversely related to damper current. Noting the difference in
-axis scales between
Figure 6a,b, with greater mass comes greater settling time, which is anticipated as the decay constant
for a typical dynamic system decreases with increased mass.
Of greater concern to us than the displacement of the leg is the impact force, given this can directly result in failure of robot parts or components, also gradually causing damage through fatigue. For the 2.65 kg total mass, the measured leg impact force
is reported in
Figure 7. Starting with the 100 mm drop height,
Figure 7a reflects the displacement behaviour observed in
Figure 4a. In particular, the ballistic flight of the rigid leg as it bounced can be observed here too where the force reduced to zero. As expected, this rigid leg and the bouncing behaviour also resulted in the greatest impact force, reaching 123 N in this case. Secondary to this were the passive control modes, reducing in force from 3 A to 0 A, followed by the no damper case with a peak impact force of 59.9 N. The other notable behaviour, present in all tests other than those of the rigid leg, was the initial peak in the force prior to the subsequent and usually largest peak. Based on observations made during testing, it seems the angle of the draw cable between the lower leg segment and variable stiffness mechanism was close to 0° from the
-axis. This made the leg relatively stiffer for the few millimetres of deflection, explaining the short rise in force which subsides until the maximum deflection of the leg was reached.
Although impact force increased in tests shown between
Figure 7a,c, it was not until that in
Figure 7d when the first collision with the ground occurred for the no damper case. While the displacement of the leg shown in
Figure 4c indicates collision occurred, it is a marginal case here, given no substantial secondary peak in impact force was observed. From
Figure 7d–f, however, this peak became very obvious, even surpassing the peak force of the rigid case for the 600 mm drop height where a value of 242 N was reached. While the peak force of the rigid cases was always exceptionally high, for these greater drop heights with this mass, it is evident the no damper case also provided unsatisfactory performance. When the leg made use of the designed passive control modes, a more reasonable range of peak force between about 75 N to 140 N was maintained. Here it is found that the 0 A case consistently provided the optimal performance over other passive currents, always resulting in the minimum peak force for the MRVSAL-II. For the 600 mm drop height, this represents a reduction in peak force of 20.1% from the 3 A force of 135 N to 0 A force of 108 N.
In contrast to the impacts with the lower mass, the tests conducted with the 4.60 kg total mass, included in
Figure 8, indicate collision occurs for the no damper case in all tests. Where no such collision occurred, compared with the 2.65 kg total mass tests, peak impact force for all tests was increased by a factor of roughly 1.5, somewhat lower than the 1.74 factor by which the mass was increased. Of more relevance to managing these impacts, however, it is observed that no collision occurred for any passive control mode for the 100 mm and 200 mm drop heights, included in
Figure 8a,b, respectively. Where it was challenging to distinguish from displacement data alone in
Figure 5c, here in
Figure 8c, the corresponding 300 mm tests showed that the passive control modes also started to result in collisions. Where impacts with lower mass or drop heights previously indicated the 0 A passive control mode was always optimal, it is evident here that it was the worst-performing current setting. In contrast to the recorded 241 N peak force of the 0 A case, a reduction of 37.3% to 151 N was obtained through the 3 A case. While some variation between other passive control modes was found for greater drop heights, it can be seen from
Figure 8d–f that the minimum peak impact force was consistently obtained for the MRVSAL-II by the 3 A current setting. It can also be observed that when significant collisions did occur, i.e., those seen here beyond 300 mm drop heights, the no damper case actually resulted in a lower impact force. Although, coupled with a lower effective damping coefficient, as indicated by the longer settling times of
Figure 6b, impact energy was dissipated over a longer period for the no damper case.
To provide a good indication of impact protection performance for the passive control modes,
Figure 9 includes the peak impact force
for all tests. Considering the low mass tests,
Figure 9a shows that with the exception of the 100 mm to 400 mm drop height range, the passive control modes resulted in lower peak impact forces than the very soft no damper mode and very stiff rigid mode. With the 0 A current always resulting in the minimum peak impact force for the passive control modes, both 0 A and 1 A also outperformed the no damper mode at a 400 mm drop height. Where things vary quite a bit more is for the large mass tests, as summarised in
Figure 9b. Being mindful of the
-axis scale, once again, the impact forces recorded here readily surpassed those of the lower mass tests. It is also clear that a transition occurred for the passive control modes between the 200 mm and 400 mm drop heights, corresponding to where ground collisions started to occur in these tests as the leg began to stroke out. Beyond 200 mm drop heights with a mass of 4.60 kg or more, the leg’s stiffness and damping can therefore be considered insufficient to cushion impacts and prevent collision.