Risk-Aware Kinodynamic Motion Planning Under Uncertainty For Safe Navigation on Planetary Environments

For autonomous space exploration, robotic agents need to perform motion planning in which environmental interactions may be unknown. Learning these interactions, such as terrain mechanics for wheeled robots, can introduce uncertainties that lead to risky motion plans and potentially hazardous operations or mission failures. Moreover, uncertainties induced by perception-based systems can exacerbate the problem of safe motion planning. In this letter, we address the problem of performing cost-optimal kinodynamic motion planning with risk awareness. We approach this in two steps. First, a sampling-based planner (AO-RRT) generates a dynamically feasible, risk-aware, and asymptotically cost-optimal trajectory. Second, we formulate motion planning as a nonlinear optimization problem and solve it using sequential convex programming (SCP), using the AO-RRT trajectory as an initial solution. By quantifying risk using conditional value-at-risk (CVaR), we demonstrate a reduction in risk by over $\sim$97\% across trajectories in simulation and hardware experiments.

Maximal Controlled Invariant-MPC: Enhancing Feasibility and Reducing Conservatism through Terminal CBF Constraint in Safety-Critical Control

Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a computationally intractable problem. Therefore, approaches that can guarantee safety while reducing conservatism will help improve the optimality of the system under consideration. Here, we present a Model Predictive Control (MPC) formulation using CBF as a terminal constraint, which is proven to improve feasibility and reachable sets with increasing prediction horizon. The constructive nature of the proofs allows for warm-starting the nonlinear optimization problem, thereby reducing the computational time substantially. Simulations are set up for a simple nonholonomic system to numerically validate the results, and it is observed that the number of infeasible points decreased by a factor of 1.7 to 2.7. The increase in reachable state space was demonstrated by the ability of the system to track trajectories that are entirely inside the unsafe region of the control barrier function.

Exact and Approximate Convex Reformulation of Linear Stochastic Optimal Control with Chance Constraints

In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the state vector to encode moment information explicitly, the formulation captures linear chance constraints on states and controls across multiple time steps exactly, without conservatism, yielding strict improvements in both feasibility and optimality. For quadratic chance constraints, we derive convex approximations that are provably less conservative than existing methods. We validate the framework on minimum-snap trajectory generation for a quadrotor, demonstrating that the proposed approach remains feasible at noise levels an order of magnitude beyond the operating range of prior formulations.