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Collision-tolerant trajectory planning is the consideration that collisions, if they are planned appropriately, enable more effective path planning for robots capable of handling them. A mixed integer programming (MIP) optimization…
We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To…
In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that…
Autonomous highway driving involves high-speed safety risks due to limited reaction time, where rare but dangerous events may lead to severe consequences. This places stringent requirements on trajectory planning in terms of both…
A common sensing problem is to use a set of stationary tracking locations to monitor a collection of moving devices: Given $n$ objects that need to be tracked, each following its own trajectory, and $m$ stationary traffic control stations,…
Learning-based control methods utilize run-time data from the underlying process to improve the controller performance under model mismatch and unmodeled disturbances. This is beneficial for optimizing industrial processes, where the…
Sums-of-squares (SOS) optimization is a promising tool to synthesize certifiable controllers for nonlinear dynamical systems. Building upon prior works, we demonstrate that SOS can synthesize dynamic controllers with bounded suboptimal…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous…
We present an evaluation of several representative sampling-based and optimization-based motion planners, and then introduce an integrated motion planning system which incorporates recent advances in trajectory optimization into a sparse…
This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed…
Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new…
Closed-loop optimal control design for high-dimensional nonlinear systems has been a long-standing challenge. Traditional methods, such as solving the associated Hamilton-Jacobi-Bellman equation, suffer from the curse of dimensionality.…
Robotic systems, particularly in demanding environments like narrow corridors or disaster zones, often grapple with imperfect state estimation. Addressing this challenge requires a trajectory plan that not only navigates these restrictive…
In this paper we propose a hierarchical controller for autonomous racing where the same vehicle model is used in a two level optimization framework for motion planning. The high-level controller computes a trajectory that minimizes the lap…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Trajectory optimization with contact-rich behaviors has recently gained attention for generating diverse locomotion behaviors without pre-specified ground contact sequences. However, these approaches rely on precise models of robot dynamics…
Guaranteeing safe behavior on complex autonomous systems -- from cars to walking robots -- is challenging due to the inherently high dimensional nature of these systems and the corresponding complex models that may be difficult to determine…
This paper studies real-time motion planning and control for ball bumping motion with quadruped robots. To enable the quadruped to bump the flying ball with different initializations, we develop a nonlinear trajectory optimization-based…