What's Safe

What’s Safe is an ongoing response to Toronto’s social distancing measures. It is a dance score documented cinematically in Trinity Bellwoods Park, with movements inspired by Deepa Iyer’s framework (Mapping Our Roles in Social Change Ecosystems, 2020) and Jay Pitter’s open letter to Canadian urbanists (A Call to Courage, 2020). The project was conceived, performed, and captured by the authors of this paper. The two dancers, our second and third authors, engage in creative problem-solving by facing the reality of socially-distant grounds for play and suggesting a different type of productivity, one which is conducive to individual and social growth. The movements are then captured by our multimedia creator (or fourth author), while our artist-researcher (first author) curates and provides critique throughout. The final project considers artistic practice in response to social change as informed by (un)productivity. It uses productive imagination (e.g., play, improvisation, creative problem-solving) to investigate parameters of safety (e.g., surveillance, control, space). Through the dancers’ improvisations, we attempt to navigate these tensions and better position ourselves in relation to our current socio-geographical circumstances.

Collision Avoidance of a Kinodynamically Constrained System from Passive Agents

Robot motion planning in dynamic environments is significantly difficult, especially when the future trajectories of dynamic obstacles are only predictable over a short time interval and can change frequently. Moreover, a robot’s kinodynamic constraints make the task more challenging. This paper proposes a novel collision avoidance scheme for navigating a kinodynamically constrained robot among multiple passive agents with partially predictable behavior. For this purpose, this paper presents a new approach that maps collision avoidance and kinodynamic constraints on robot motion as geometrical bounds of its control space. This was achieved by extending the concept of nonlinear velocity obstacles to incorporate the robot’s kinodynamic constraints. The proposed concept of bounded control space was used to design a collision avoidance strategy for a car-like robot by employing a predict-plan-act framework. The results of simulated experiments demonstrate the effectiveness of the proposed algorithm when compared to existing velocity obstacle based approaches.

Normal forms for the endpoint map near nice singular curves for rank-two distributions

Given a rank-two sub-Riemannian structure $(M,\Delta)$ and a point $x_0\in M$, a singular curve is a critical point of the endpoint map $F:\gamma\mapsto\gamma(1)$ defined on the space of horizontal curves starting at $x_0$. The typical least degenerate singular curves of these structures are called \emph{regular singular curves}; they are \emph{nice} if their endpoint is not conjugate along $\gamma$. The main goal of this paper is to show that locally around a nice singular curve $\gamma$, once we choose a suitable topology on the control space we can find a normal form for the endpoint map, in which $F$ writes essentially as a sum of a linear map and a quadratic form. This is a preparation for a forthcoming generalization of the Morse theory to rank-two sub-Riemannian structures.