Experimental results

The offline evaluation of the detection algorithms is described below, based on the previous preliminary settings. As a reminder, the experiment in Section 4.1.1 involves four impacts of different amplitude, which effects on the residual may be of the same order of magnitude as the peaks due to modeling uncertainties. The objective in the following is to compare the results obtained with the different impact detection algorithms in order to highlight the advantages and disadvantages of each method.

The estimated external torque ˆτext and its associated detection thresholds are illustrated for

axis 2 inFigure 4.13for the DETE-based method and the JPVO and GMO, all being computed in the rigid case because the robot elasticities were not “strongly” stimulated along the trajectory. As described in Chapter 3: "Design of impact detection strategies under model uncertainties", the envelope formed by the positive and negative detection thresholds Tk_{= ± 3 σ}

e(k) represents

at each time step the maximum contribution of the uncertainties in absence of external contact. Consequently, when one of these thresholds is exceeded, it necessarily implies that there is an additional contribution due to an external contact (in 99.7% of the cases for the 3σ-confidence interval). The induced alarm signal, which is triggered as soon as one of the components of ˆτext

exceeds its thresholds, is displayed for each method in relation with the applied force as measured by the force/torque sensor in Figure 4.14. The corresponding detection times are reported in the associated tables. For disturbance observers, the results are given for the Kalman filter that provides the earliest detection, which parameters are specified in the associated tables.

The peaks on the detection thresholds that can be observed in Figure 4.13 correspond to low- speed transitions below αq (e. g. change in the trajectory direction) during which the sign of the

measured velocity may be different from the sign of the robot’s actual velocity. This generates a peak of error on the residual, which is noticeable for the DETE, but for disturbance observers, the transition being fast, it is not visible on the estimate output. Nonetheless, to account for this error, the detection thresholds increase accordingly during that period of time, which makes the detection of an impact occurring at this moment less sensitive.

We observe that the strongest impacts (impacts 1 and 4) are correctly detected by all three methods. However, when the impact is of lower amplitude (impacts 2 and 3), the three detection methods barely detect it. In particular, impact 3 is only detected by the GMO, which makes it the most sensitive algorithm in this situation. In addition, the residual provided by the DETE is quite noisy and would probably be unusable as it stands for further developments (e. g. location of the contact point, reconstruction of the applied force) without prior filtering. Conversely, the Kalman filtering estimates are more filtered and reusable.

Regarding the Kalman filters bank adjusted with different disturbance models, the combination (Aext = 0, Σext = I) is the one that actually gives the longest detection times (e. g. for impact 4,

we get 1.519s for the JPVO and 1.288s for the GMO), while for (Aext = 5I, Σext = 100I),

corresponding to the least sensitive adjustment, only impact 4 is detected for both observers since this is the strongest impact. Finally, the combination (Aext = 0, Σext = 100I) provides the

4.1. Validation and characterization of detection performance 117

Figure 4.13: Residual (estimation ˆτextof the external torque) obtained in the rigid case with the

DETE, the JPVO and the GMO (with disturbance model A1, Σ3) and its associated detection thresholds. Impact times are indicated by the shaded areas. In red are indicated the points above the thresholds that trigger a detection alert.

Method Detection time Disturbance model

DETE 0.591 s –

JPVO 1.272 s A1, Σ3

GMO 1.081 s A1, Σ3

(a) Results for impact 1

Method Detection time Disturbance model

DETE 1.150 s

JPVO 2.071 s A1, Σ3

GMO 1.460 s A1, Σ3

(b) Results for impact 2

Method Detection time Disturbance model

DETE –

JPVO – –

GMO 1.991 s A1, Σ3

(c) Results for impact 3

Method Detection time Disturbance model

DETE 0.333 s

JPVO 0.938 s A1, Σ3

GMO 0.825 s A2, Σ3

(d) Results for impact 4 Alert signals:

Figure 4.14: Alert signals (dashed lines) indicating the impact detection (impact if > 0 ) in relation with the applied force measured by the force/torque sensor (solid black line). The corresponding detection times are reported in the associated tables.

4.1. Validation and characterization of detection performance 119

The analytical criteria of settling time and expected sensitivity threshold are derived for this experiment for axis 2 inFigure 4.15. Note that the settling time for the DETE is not illustrated but given the absence of filtering, the rise time is very fast, making this method the fastest regardless of the disturbance observers adjustment. The actual external torque τext, induced

by the wrench measured by the force/torque sensor and transmitted at the joint-level with equation (2.1), is also reported for comparison with the algorithms sensitivity. The frequency- domain analysis confirms that the response time of ˆτext with the GMO is faster than with the

JPVO, the latter being probably affected by a penalizing delay on the acceleration estimates due to the pessimistic settings of ωc = 2π10 rad/s. The sensitivity analysis of these algorithms shows

that for some adjustments of the disturbance model parameters, the two observers can provide a better detection sensitivity than the DETE. However, this sensitivity is achieved at the cost of a relatively long detection time. Indeed, in the case of impact 3, the input torque τext starts to

decrease before the JPVO estimate has reached the detection threshold (seeFigure 4.13), which is why this impact is not detected by the JPVO as it should be according toFigure 4.15b.

:

(a) Settling times

:

(b) Minimum detectable torques and actual external torque Figure 4.15: Analytical criteria for the DETE, the JPVO and the GMO (with disturbance model

A1, Σ3). Impact times are indicated by the shaded areas.

Finally, from the previous frequency-domain analysis and these experimental results, we can con- sider that the DETE is advantageous for its detection rapidity, while disturbance observers JPVO and GMO are interesting to achieve a sensitive detection. The comparison between these two observers depends on the levels of acceleration involved during the robot’s trajectory. Besides, the output of the observers being filtered, it is more directly reusable for further developments than the residual computed with the DETE.

However, the comparison of detection times gives an idea of the algorithms reactivity but does not provide information about the contact dangerousness. Indeed, a severe impact that is rapidly detected may be as dangerous as an impact of low amplitude but detected late. In addition, at identical detection times, an impact will not produce the same effects depending on the robot speed or the type of environment collided. Therefore, the next section proposes to investigate the energy dissipated by the robot and the environment during the contact and to determine the amount of energy absorbed by the collided object.