Robot navigation in dense crowds : statistical models and experimental studies of human robot cooperation

This thesis explores the problem of mobile robot navigation in dense human crowds. We begin by considering a fundamental impediment to classical motion planning algorithms called the freezing robot problem: once the environment surpasses a certain level of complexity, the planner decides that all forward paths are unsafe, and the robot freezes in place (or performs unnecessary maneuvers) to avoid collisions. Since a feasible path typically exists, this behavior is suboptimal. Existing approaches have focused on reducing predictive uncertainty by employing higher fidelity individual dynamics models or heuristically limiting the individual predictive covariance to prevent overcautious navigation. We demonstrate that both the individual prediction and the individual predictive uncertainty have little to do with this undesirable navigation behavior. Additionally, we provide evidence that dynamic agents are able to navigate in dense crowds by engaging in joint collision avoidance, cooperatively making room to create feasible trajectories. We accordingly develop interacting Gaussian processes, a prediction density that captures cooperative collision avoidance, and a "multiple goal" extension that models the goal driven nature of human decision making. Navigation naturally emerges as a statistic of this distribution.

Most importantly, we empirically validate our models in the Chandler dining hall at Caltech during peak hours, and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (collecting data on 488 runs). The multiple goal interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities nearing 1 person/m², while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as the multiple goal extension, and twice as often as the basic interacting Gaussian process approach. Furthermore, a reactive planner based on the widely used dynamic window approach proves insufficient for crowd densities above 0.55 people/m². We also show that our noncooperative planner or our reactive planner capture the salient characteristics of nearly any dynamic navigation algorithm. For inclusive validation purposes, we show that either our non-interacting planner or our reactive planner captures the salient characteristics of nearly any existing dynamic navigation algorithm. Based on these experimental results and theoretical observations, we conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.

Finally, we produce a large database of ground truth pedestrian crowd data. We make this ground truth database publicly available for further scientific study of crowd prediction models, learning from demonstration algorithms, and human robot interaction models in general.

Mechanisms of substrate selection by the signal recognition particle

The signal recognition particle (SRP) targets membrane and secretory proteins to their correct cellular destination with remarkably high fidelity. Previous studies have shown that multiple checkpoints exist within this targeting pathway that allows ‘correct cargo’ to be quickly and efficiently targeted and for ‘incorrect cargo’ to be promptly rejected. In this work, we delved further into understanding the mechanisms of how substrates are selected or discarded by the SRP. First, we discovered the role of the SRP fingerloop and how it activates the SRP and SRP receptor (SR) GTPases to target and unload cargo in response to signal sequence binding. Second, we learned how an ‘avoidance signal’ found in the bacterial autotransporter, EspP, allows this protein to escape the SRP pathway by causing the SRP and SR to form a ‘distorted’ complex that is inefficient in delivering the cargo to the membrane. Lastly, we determined how Trigger Factor, a co-translational chaperone, helps SRP discriminate against ‘incorrect cargo’ at three distinct stages: SRP binding to RNC; targeting of RNC to the membrane via SRP-FtsY assembly; and stronger antagonism of SRP targeting of ribosomes bearing nascent polypeptides that exceed a critical length. Overall, results delineate the rich underlying mechanisms by which SRP recognizes its substrates, which in turn activates the targeting pathway and provides a conceptual foundation to understand how timely and accurate selection of substrates is achieved by this protein targeting machinery.

Convex model predictive control for vehicular systems

In this work, the author presents a method called Convex Model Predictive Control (CMPC) to control systems whose states are elements of the rotation matrices SO(n) for n = 2, 3. This is done without charts or any local linearization, and instead is performed by operating over the orbitope of rotation matrices. This results in a novel model predictive control (MPC) scheme without the drawbacks associated with conventional linearization techniques such as slow computation time and local minima. Of particular emphasis is the application to aeronautical and vehicular systems, wherein the method removes many of the trigonometric terms associated with these systems’ state space equations. Furthermore, the method is shown to be compatible with many existing variants of MPC, including obstacle avoidance via Mixed Integer Linear Programming (MILP).

Imperfection Insensitive Thin Shells

The buckling of axially compressed cylindrical shells and externally pressurized spherical shells is extremely sensitive to even very small geometric imperfections. In practice this issue is addressed by either using overly conservative knockdown factors, while keeping perfect axial or spherical symmetry, or adding closely and equally spaced stiffeners on shell surface. The influence of imperfection-sensitivity is mitigated, but the shells designed from these approaches are either too heavy or very expensive and are still sensitive to imperfections. Despite their drawbacks, these approaches have been used for more than half a century.

This thesis proposes a novel method to design imperfection-insensitive cylindrical shells subject to axial compression. Instead of following the classical paths, focused on axially symmetric or high-order rotationally symmetric cross-sections, the method in this thesis adopts optimal symmetry-breaking wavy cross-sections (wavy shells). The avoidance of imperfection sensitivity is achieved by searching with an evolutionary algorithm for smooth cross-sectional shapes that maximize the minimum among the buckling loads of geometrically perfect and imperfect wavy shells. It is found that the shells designed through this approach can achieve higher critical stresses and knockdown factors than any previously known monocoque cylindrical shells. It is also found that these shells have superior mass efficiency to almost all previously reported stiffened shells.

Experimental studies on a design of composite wavy shell obtained through the proposed method are presented in this thesis. A method of making composite wavy shells and a photogrametry technique of measuring full-field geometric imperfections have been developed. Numerical predictions based on the measured geometric imperfections match remarkably well with the experiments. Experimental results confirm that the wavy shells are not sensitive to imperfections and can carry axial compression with superior mass efficiency.

An efficient computational method for the buckling analysis of corrugated and stiffened cylindrical shells subject to axial compression has been developed in this thesis. This method modifies the traditional Bloch wave method based on the stiffness matrix method of rotationally periodic structures. A highly efficient algorithm has been developed to implement the modified Bloch wave method. This method is applied in buckling analyses of a series of corrugated composite cylindrical shells and a large-scale orthogonally stiffened aluminum cylindrical shell. Numerical examples show that the modified Bloch wave method can achieve very high accuracy and require much less computational time than linear and nonlinear analyses of detailed full finite element models.

This thesis presents parametric studies on a series of externally pressurized pseudo-spherical shells, i.e., polyhedral shells, including icosahedron, geodesic shells, and triambic icosahedra. Several optimization methods have been developed to further improve the performance of pseudo-spherical shells under external pressure. It has been shown that the buckling pressures of the shell designs obtained from the optimizations are much higher than the spherical shells and not sensitive to imperfections.