This chapter presented three kinds of acceleration profiles adopted in this work. They serve for the vehicle’s smooth transition between different accelerations, its acceleration keeping and its reaching a specific state, respectively. These acceleration profiles are designed based on the theory of trajectories of minimum jerk. They are associated with the path edges to generate trajectory edges during the construction of the trajectories.
The association approach applied in the proposed planner is helpful in improving the smoothness of the resultant trajectory from the perspective of a standalone planning horizon. Its main idea is to allow one acceleration profile to expand over several path edges, which distinguishes it from the approaches applied in similar works, where one acceleration profile can at most cover one edge.
In sum, the proposed trajectory representation strategy is distinguished in the smooth acceleration profiles and a method of associating multiple consecutive edges and one ac-celeration profile. This strategy can improve the feasibility of the trajectories generated by the planner.
Speed(m/s)
(a) Trajectories of speed, acceleration and jerk during an accelerating motion (ktrans= 0.5).
(b) Trajectories of speed, acceleration and jerk during an accelerating motion(ktrans= 2).
Figure 4.6: Uniform polynomials and multi-piece trajectories of speed, accel-eration and jerk during three typical vehicle motions. The red curves are the results of the uniform polynomial. The blue curves demonstrate the behaviour of the planner.
Speed(m/s)
(c) Trajectories of speed, acceleration and jerk during a decelerating-accelerating motion (ktrans= 2).
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(d) Trajectories of speed, acceleration and jerk during a decelerating motion (ktrans= 1).
Figure 4.6: Uniform polynomials and multi-piece trajectories of speed, accel-eration and jerk during three typical vehicle motions. The red curves are the results of the uniform polynomials. The blue curves demonstrate the behaviour of the planner.
Motion Planner Implementation and System Integration
This chapter describes the implementation of the proposed motion planner. Section5.2 shows how the motion planning strategy and algorithms presented in the previous two chapters can be put into practice to generate an effective and practical motion planner.
Besides, it lists the cost functions devised and implemented in the proposed planner.
Section5.3begins with an introduction to the planning system of MIG and the interfaces between different planning modules. Then, the integration of the proposed planner into the planning system of MIG is demonstrated. Finally, the measures adopted to compensate for the planning latency and to promote the planning consistency between successive planning horizons are illustrated. Before that, we firstly take a look at how to define the planning horizon and the durations of the planning cycles.
5.1 Planning Horizons and Durations of Planning Cycles
At the start of each planning cycle, a planning horizon should be specified where the sampling can be performed. In the context of motion planning in the spatiotemporal space, the planning horizon is twofold: the temporal horizon embodied by a period of time and the spatial horizon consisting of road segments within a travel distance. Let the temporal horizon, the spatial horizon and the duration of one planning cycle be denoted asHT,HS and CT respectively. HT,HS andCT are among the most important design parameters of a motion planner. HScontains several aspects itself, such as its extending distancedH, the number of the road segmentsnseg within its domain, the width of each road segment wseg, etc. The strategy for specifying the road segments is discussed in the next section and is assumed given here. Consequently, among the aspects of HS, onlydH remains to be influenced; the others are decided by the method of specifying the road segments and the practically unchangeable road layout. As a result, the following focuses on how to specify HT,dH and CT.
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In general, the values of design parameters should be decided based on the evalu-ation criteria and constraints of the design. Recall that the performance indexes of a motion planner includecompleteness,feasibility,optimality and computational complex-ity (cf. Subsection 1.3). The criterion optimality can be further divided into horizon optimality, scenario optimality and resolution optimality (cf. Subsection 1.3). Among those six criteria, horizon optimality and computational complexity are directly related to the choices of HT, HS and CT. Assuming that an intra-horizon planning strategy is given and that the vehicle’s perception of the surrounding traffic is ideally sufficient, it is straightforward that an extensive planning horizon would improve the condition of horizon optimality. Due to limited computational resources, however, motion planning in an extensive planning horizon would inevitably require a longCT, which is impracti-cal due to safety concerns. The real-life traffic can be highly dynamic, and the vehicle’s actual sensing ability is still limited. As a result, it is necessary for the motion planner to update its plans at a high frequency so that it can react quickly to newly perceived information. Considering all the factors mentioned above, the guidelines for choosing HT,dH andCT are outlined as follows:
• From the perspective of horizon optimality, CT should be as large as possible.
Conversely, the safety requirement imposes a limit on the upper bound of CT. As a result, CT is determined based on the safety requirement. This constraint is obtainable from a comprehensive assessment of the vehicle’s sensing and predicting ability and the complexity of the traffic environment.
• The lower bound ofHT should be no less thanCT as the vehicle must have a plan to follow while the motion planner is working on a new plan. In other words, it is required that the time domain of the trajectory generated from the last planning cycle should at least cover the duration of the current planning cycle. Given an average vehicle speed within the planning horizon, the lower bound ofdH can be calculated according to the lower bound ofHT
• As the computational complexity can be expressed in terms of all the aspects of HS,dH can be derived as an expression in terms of the computational complexity and the remaining aspects. Note that the maximum computational complexity in terms of time should not exceed CT. Consequently, the upper bound of dH can be determined by a comprehensive effect of CT and the road layout aspects of HS. Again, given an average vehicle speed within the planning horizon, the upper bound ofdH can be used to set the upper bound of HT. In this way, the value of CT and the ranges of HT anddH can be determined.
The concrete application of those principles listed above in determiningCT,HT and dH requires lots of experiments and repetitive adjustments, which is beyond the scope
Parameter Value Parameter Value
Station increments 10 Station interval 10m
Lattitude increments 20 Lateral offset 0.5m
Outgoing paths of a single spatial node
18 Sampling unit of the XYSL Map 0.5m×0.5m Acceleration profiles 8 Spatial sampling unit of the cost
maps
0.5m×0.5m
Time discretizations 2 Path sampling step 0.5m
Speed discretizations 4 Frames of the dynamic cost map 20 Table 5.1: Parameters of the example state lattice
of this work. Accordingly, it is assumed in this thesis that reasonable values of CT,HT and dH are given.