Motion Generation With Environmental Constraints

Robot motion planning is inherently multimodal, yet classical planners typically return only a single solution. Probabilistic formulations address this limitation by maintaining a distribution over motions, allowing the planner to reason over multiple low-cost alternatives. In robotics, however, motion samples must also satisfy strict constraints, including collision avoidance, joint limits, contact conditions, and dynamics consistency. These hard requirements make motion sampling substantially more challenging: within a limited planning budget, the ensemble must cover diverse low-cost motions while ensuring that every sample remains feasible under the relevant constraints. We propose SteinSQP (Stein Variational Sequential Quadratic Programming), a constrained Stein variational inference method for diverse feasible robot motion sampling. SteinSQP evolves an interacting particle ensemble, as in Stein variational methods, while embedding constraints directly into a kernel-space SQP subproblem. We solve the resulting constrained Stein-Newton subproblem with a GPU-friendly matrix-free primal-dual algorithm, enabling efficient batched ensemble updates. To globalize the method, we introduce an ensemble-level merit function that jointly balances objective value, constraint violation, and particle diversity. Across five constrained motion-planning tasks, SteinSQP returns fully feasible ensembles while preserving diverse motion alternatives. Compared with first-order constrained Stein baselines and serial multistart nonlinear programming, SteinSQP shows faster and more robust ensemble convergence in terms of iterations, improves particle-wise feasibility, and achieves faster batched time-to-solution on challenging robot-scale tasks.

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.

Motion planning algorithms compute control sequences that drive autonomous robots to goal regions while avoiding unsafe states. Existing methods, from sampling-based planning to deep reinforcement learning, typically provide task-completion guarantees only with respect to a nominal model or simulator, which may be invalidated when the true dynamics are unknown or difficult to model accurately. This letter addresses this limitation for systems with unknown dynamics and an available approximate nominal model, contributing a planner-agnostic constraint-tightening procedure that equips existing planners with a probabilistic task-completion guarantee on the true system. We leverage conformal prediction to provide a probabilistic bound on the nominal-to-true trajectory deviation over a distribution of planning problems. We tighten the planning constraints using that bound, and show that solving the tightened problem under the nominal model is a sufficient condition for solving the original problem on the true system with a prescribed probability. We validate the theoretical guarantees empirically and demonstrate substantially improved task completion relative to nominal-model planning.