In this paper we have presented a practical approach to path planning with control uncertainty on unstruc-tured terrain. We used Gaussian processes to build continuous, stochastic mobility prediction models from empirical data. These models provided a stochastic transition function to an MDP-based planning algorithm, which used dynamic programming to build optimal policies for the rover to execute. We presented extensive empirical results that demonstrate this approach leads to more reliable and safer navigation.
Two different methods to train the stochastic mobility prediction were implemented and demonstrated. The first used proprioceptive data (LfP), and the second used exteroceptive data (LfE). To facilitate comparison of these two methods, we collect statistics that describe the overall success of each method, across all experimental trials reported in the paper, in Table 13.
Obtaining the training data for the LfP-based method was straightforward, as it simply required to record the attitude and configuration angles of the rover during multiple execution of its actions. The experimental results of LfP showed that accounting for control uncertainty in the planning led to enhanced reliability on rigid terrain, as illustrated by the reduction of failed runs (see Table 13). Furthermore, the executed paths were safer, as evidenced by the significant cost reduction for the executed paths (19% and 31% when considering distance and heading uncertainty, respectively, shown in Table 4). In addition to the increased reliability and safety, the reduction in the standard deviation of the number of executed actions demonstrated improved consistency in the path execution (shown in Fig. 12). However, no clear benefit of accounting for control uncertainty was observed when using the LfP-based method on deformable terrain. Therefore, accounting for control uncertainty within the LfP method was only beneficial if no terrain deformation was
(a) No uncertainty
(b) Heading & Yaw uncertainty
Figure 22: Example of rover trajectories (coloured lines) obtained by following the policies generated by the LfE method with: (a) no control uncertainty considered, and (b) heading & yaw uncertainty. The dotted white box represents the goal region.
0
Figure 23: Average terrain cost (a) and number of actions (b) over the paths executed by the rover for experimental runs using the LfE method on the whole Mars Yard.
Table 13: Percentage of failed runs for the LfP and LfE methods Method Uncertainty
Training with the LfE-based method was more complex than for the LfP. This method required to build terrain maps and make predictions of attitude configuration angles on multiple positions along the expected path, rather than simply recording these angles from proprioceptive sensors. However, the LfE method clearly outperformed LfP. With the LfE-based method, accounting for control uncertainty in the planning strongly enhanced reliability, as the reduction in number of failed runs was greater than when using the LfP method2(shown in Table 13). The executed paths were also safer, as shown by the cost reduction of 25% and 41% for executed paths considering distance and heading uncertainty, respectively (Table 8). In addition, the paths executed were more consistent, especially when considering heading uncertainty, as demonstrated by the reduced standard deviation in the number of executed actions to reach the goal (Fig. 18). On deformable terrain the LfE-based method also showed enhanced reliability and safety when accounting for uncertainty, as evidenced by the strong reduction of failed runs (Table 9) and a clear cost reduction for executed paths (12% and 16%, shown in Table 10). These results were even stronger for longer runs, with a cost reduction of 41% and a reduction of the number of failed runs by half obtained when considering heading uncertainty, as shown in Sec. 7.3.3. Therefore, accounting for control uncertainty within the LfE method proved beneficial in all the situations considered, including when the rover experienced terrain deformation. These results can be explained by better consistency between the predicted features λ∗ used in planning and the features λtrain extracted from the training data. In conclusion, the results in this paper empirically validate the importance of coupling terrain profile features with control uncertainty.
Although accounting for control uncertainty in the planning allowed for a significant reduction of failed
2This comparison is valid because the experimental tests have been run in the same conditions for both methods.
experimental runs, especially using the LfE method, some failures remained when the rover had to traverse challenging terrain. In most cases these failures were due to wheel slippage preventing a wheel from over-coming a rock. Slip is not captured directly in our cost function, but instead as control uncertainty in the stochastic transition model. Therefore, the rover is not necessarily avoiding such areas if it was capable of traversing comparable areas sufficiently often in the training phase. The rover may be aware that a particular action has some probability of falling short, but not that this may actually corresponds to it being stuck for indefinite time. In future work, we may consider incorporating the risk of extreme slip in the cost function, and explicitly account for the risk of overall failures in the planning stage.
So far, we have considered individual dimensions of control outcomes independently, and shown that heading and distance uncertainty both contribute to safer navigation. In future work, we will consider the case where these predictions are correlated. This case is a natural extension of our learned mobility prediction model, but will require a more complex regression technique. One possibility for this purpose is multi-output GP (Boyle and Frean, 2005). We will also consider uncertainty in the cost map and the localisation, in addition to the control uncertainty. A specific study of the trade-off between training and performance will also be conducted. Finally, to facilitate the implementation of such approach in practice when the rover has to be deployed in terrain whose type is a priori largely unknown, we will consider on-line training strategies.
Acknowledgments
This work was partly supported by the Australian Government’s DIISR grant “Australian Space Research Program”, the Australian Centre for Field Robotics (ACFR) and the New South Wales State Government.
This material is also based on research partially sponsored by the Air Force Research Laboratory, under agreement number FA2386-10-1-4153. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.
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