Moving targets

Many active perception problems involve perceiving moving targets, such as in track- ing, search, and pursuit-evasion (Chung et al., 2011; Robin and Lacroix, 2015), as well as the mission monitoring problem introduced in Chapter 5. The targets may be, e.g., robots, humans, or animals. Observation prediction models in this context require predicting the dynamic states of the targets, or trajectory prediction. In this subsection, we review trajectory prediction models, and then later in Section 5.8 and Appendix A we propose new example models used as prediction models for evaluating our planning algorithms.

Prediction models

Approaches to the trajectory prediction problem largely depend on the underlying assumptions about the motion of the agent or object of interest. The simplest as- sumption is that the agent is stationary, which may be appropriate for some appli- cations (Xu et al., 2013; Hönig and Ayanian, 2016), but would require constantly replanning as the scene changes.

Another simple assumption is that the agent will continue moving with constant or near-constant velocity or acceleration (Chiang et al., 2014; Reece and Roberts, 2010).

These assumptions allow for efficient computation and may be a sufficient prediction model to improve performance in tracking applications. However these simple models are often insufficient for dynamic collision avoidance applications where performance is highly dependent on the accuracy of the predictions rather than the accuracy of the current position estimate, particularly when extrapolating relatively far into the future.

Similar models can be extended to model multi-agent collision avoidance in crowds, which is a highly-active area of research (Lerner et al., 2007; Pellegrini et al., 2009; Yamaguchi et al., 2011; Trautman et al., 2013; Kim et al., 2015). Due to the com- pounded uncertainty of crowds these predictions are usually only reliable in the very near future.

Another common assumption is that the agent will reliably follow one of possibly many predefined paths, which may come from training data based on previous agent trajectories (Bruce and Gordon, 2004; Aoude et al., 2013) or known mission plans (Section 5.8.1). For the case where there are multiple possible predefined paths, the predictions are characterised by a multi-modal distribution. Furthermore, the predictions can be improved by estimating which single paths out of all possible paths is the agent more likely to be following (Bruce and Gordon, 2004; Aoude et al., 2013; Ahmad et al., 2016). The benefit of this approach is that any underlying assumptions about the agent’s motion, such as probabilistic dynamics and velocity constraints, can be modelled implicitly within the predefined paths. However, most realistic scenarios are less predictable and therefore it is impractical to find a small discrete set of paths that accurately model the possible paths of the agent.

In the trajectory prediction model we propose in Appendix A, we reason over a po- tentially infinite number of paths that the agent could possibly take. However we group together all paths that have a common end position and then predictions are performed by first updating a belief for the end position of the agent’s path. If the end position is known then this information can be used to improve the predictions (Pelle- grini et al., 2009). However, in most cases the end position is not known and therefore it is advantageous to instead maintain a belief over all possible end positions based on observations or training data.

Intention inference

An agent is often guided by an underlying intention to move to another specific region of the environment. In this sense, each movement taken by the agent can be thought of as an action leading towards achieving the underlying intention to move to a goal region of the environment. This falls into the scope of plan recognition (Charniak and Goldman, 1993; Goldman et al., 1999). General approaches to plan recognition are formulated around the idea that every observed action gives information about higher-level objectives, while reasoning over the higher-level objectives in turn gives information to predict future actions. Example applications of plan recognition in robotics includes robot table tennis, interactive humanoid robots (Wang et al., 2013) and inferring the plan of wheelchair operators (Huntemann et al., 2013).

The plan recognition concept has been used to formulate solutions to trajectory pre- diction problems. Some interesting proposed methods use a general definition of the agent’s intention and therefore allow the use of more general frameworks such as POMDPs (Bandyopadhyay et al., 2012). It can also be beneficial, and computation- ally efficient, to consider a more narrow definition of intention. Kim et al. (2015) define the agent’s intention to maintain a velocity close to an unknown preferred velocity which may change slowly over time as the agent moves through a crowd, using Kalman filters and a maximum-likelihood estimate of the model parameters. Schreier et al. (2014) define intentions as typical manoeuvres while driving on struc- tured roads (e.g., changing lanes), where inference is aided by observed properties of the road (e.g., the existence of lanes). An alternative interpretation of these concepts with a fundamentally similar formulation is presented by Nishimura and Schwager (2018), where one agent aims to convey one of several possible messages to another agent through its motion. Similar concepts have also been proposed in multi-player games, known as stochastic Bayesian games, where the inferred behaviours of other agents are described as one of several possible “types” (Albrecht et al., 2016; Barrett et al., 2011).

Objectives

Formulating a perception objective function suitable for planning requires these mod- els to be reliable over a reasonably long time period. Ideally, the model should be probabilistic so planning can be performed with respect to all possible outcomes. The objective function can vary greatly from task to task, such as minimising the uncertainty of the tracking estimation (Xu et al., 2013), uncertainty of the intention inference (Nishimura and Schwager, 2018), or the distance to the agent (Švec et al., 2014). In Chapter 5 we formulate expected observation time as an objective, and we propose planners that optimise with respect to long-term probabilistic trajectory predictions.