Multi-Objective Motion Planning

As robots are increasingly deployed in groups and share workspaces to execute real-world tasks, planning their concurrent motions around complex manipulation skills becomes essential. These skills involve continuous physical execution and may exhibit stochastic behavior, resulting in variable execution times and uncertain continuous trajectories. Existing planners either limit execution to single-robot scenarios, rely on open-loop paths, or use post-hoc scheduling that prevents dynamic coordination. In this paper, we address this gap by integrating stochastic skills into sampling-based multi-robot planning by formulating the problem as a Markov Decision Process (MDP) over a multi-modal composite roadmap. For stochastic skills, solving the MDP yields a reactive policy that allows controllable robots to dynamically adapt their motions in response to other robots' execution of manipulation skills. By resolving skill uncertainty directly at planning time, this approach avoids the pessimism of conservative baselines and unlocks robust, dynamic multi-robot coordination. Code for the planners is available at https://www.vhartmann.com/stochastic-skills.

Multi-Modal Motion Planning (M$^3$P) requires joint reasoning over continuous motions and discrete mode transitions, making it difficult to solve efficiently. For instance, a bipedal robot may walk to a target location and then use its arms to grasp an object. This scenario captures both mode transitions and continuous dynamics, yielding feasible paths that neither purely discrete nor continuous planners can handle. While Mixed-Integer Programming (MIP) offers a principled framework, constructing tractable formulations for non-convex problems is typically manual and domain-specific, especially in the approximate, discretization-based MIP regime needed for non-convex robotic tasks. We propose M$^3$P-R1, a reinforcement learning method that fine-tunes large language models (LLMs) to decompose M$^3$P tasks into MIP variables, constraints, and objectives. Instead of directly outputting answers, which are often prone to hallucination, the model generates executable Python code using MIP optimization libraries and constraint interfaces. This enables solver-backed execution for robust and verifiable solutions. Trained with an outcome-driven reward against the solver, M$^3$P-R1 learns to compose modality-level discretization primitives and synthesize cross-modal coupling constraints, producing executable MIP programs for complex M$^3$P tasks.

We present the PccDiffuser, a conditional diffusion framework for continuum robots that learns a multimodal distribution over complete configuration-space paths and samples multiple candidate solutions in parallel, which are subsequently converted into an executable trajectory by time allocation considering actuator constraints. Under the piecewise constant-curvature model, we use exponential co-ordinates to describe the robot kinematics, and use graph neural network to encode a variable number of environment obstacles. Analytical differential kinematics is incorporated in the denoising process to improve terminal accuracy and whole-body clearance. On a mixed test set comprising workspace with zero to four obstacles, PccDiffuser achieved a success rate of 91%. Compared with existing sampling- and optimisation-based benchmarks, it delivered both a higher success rate and greater computational efficiency, with the latter advantage becoming more substantial when sampling more candidate solutions. Experiments on a three-section tendon-driven continuum robot further demonstrate consecutive planning, multi-solution planning, and whole-body obstacle avoidance.

This paper addresses multi-objective kinodynamic planning in environments with stochastic hybrid adversaries that probabilistically transition to adversarial modes based on the ego state. The goal is to construct the Pareto-front of paths that trade off execution cost and the probability of safety constraint violation (risk). Existing chance-constrained planners evaluate risk over open-loop trajectories, yielding overly conservative solutions that fail to account for ego-agent reactivity. To address this limitation, we shift the planning space to sequences of closed-loop policies, and integrate sample-based risk evaluation directly into tree construction via Monte-Carlo particle rollouts. We first introduce Stochastic Multi-Objective RRT (SMO-RRT), for which we prove probabilistic completeness, followed by Stochastic Multi-Objective Stable Sparse RRT (SMO-SST), which leverages selective pruning to improve numerical performance at the cost of completeness. For both algorithms, we derive a finite-sample bound on the probability of chance constraint violation for systems with non-Gaussian, state-dependent uncertainty, enabling probabilistically safe planning in a broad class of environments applicable to multi-agent systems, social navigation, and autonomous driving.

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.

Safe multi-arm motion planning is a challenging problem in robotics due to its high dimensionality, coupled configuration space, and complex collision constraints. Centralized planners are capable of coordinating all arms but often face scalability limitations, restricting applicability in real-time settings. On the other hand, decentralized methods are scalable and recent deep learning-based approaches have shown promising results. However, these depend on accurate behavior prediction or coordination protocols and may fail when other arms act unpredictably. To address these challenges, we introduce a neural Hamilton-Jacobi Reachability (HJR) learning-based approach to approximate a safety value function that captures worst-case inter-arm safety constraints. We further develop a decentralized trajectory optimization framework that uses the learned HJR representation for real-time planning. The proposed method is scalable and data-efficient, generalizes across multi-manipulator systems, and outperforms state-of-the-art baselines on challenging multi-arm motion planning tasks.

Robots deployed in the real world must plan motions across diverse scenarios without per-scenario retuning. End-to-end reinforcement learning (RL) can generalize across scenarios but often becomes brittle under distribution shift, reward misspecification, and stochastic interactions. Model predictive path integral (MPPI) control enables strong real-time refinement without gradients, but its performance depends on a well-shaped sampling prior, while manually designing the priors does not scale to multi-scenario deployment. We present HOLO-MPPI (High-level Offline, Low-level Online MPPI), a multi-scenario motion planning framework that combines high-level policy learning with low-level stochastic optimal control. Offline, we learn a high-level policy that proposes scenario-robust plans in an abstract action space, with a learned world model for online rollout. Online, the policy serves as a data-driven prior generator that parameterizes MPPI's sampling distribution conditioned on the current observation and goal. MPPI then optimizes low-level control sequences around this prior in real time to adapt to local disturbances. We instantiate HOLO-MPPI in autonomous driving by designing an effective high-level action space and tailored model architectures. Our evaluation across diverse driving scenarios shows that HOLO-MPPI improves upon MPPI and end-to-end RL baselines while maintaining real-time control.

V2X can warn an autonomous vehicle about hazards beyond line-of-sight, but it also brings uncertainty: messages may be delayed, dropped, or even forged. Meanwhile, map knowledge may change during a trip, forcing the vehicle to replan under tight real-time budgets. This paper studies how to make motion planning and low-level control robust to such uncertain, event-driven updates. We present MORPH-U, a CARLA-based closed-loop stack that fuses LiDAR/radar/camera with V2X (CAM/DENM) into a Local Dynamic Map (LDM) and triggers Hybrid-A* replanning when validated hazards or map changes affect the planned route. We expose the planning/control trade-offs via a multi-objective formulation over tracking error, safety margin (minimum TTC), responsiveness, and smoothness, and select operating points using Pareto-frontier analysis. To avoid unsafe replanning from faulty V2X triggers, MORPH-U adds a lightweight Byzantine-inspired acceptance gate that combines a quorum rule with an on-board sensor veto. Experiments in dynamic CARLA scenarios show that V2X-augmented LDM improves downstream safety, Pareto tuning provides controllable accuracy-comfort trade-offs, and the gate prevents replanning under saturated false-DENM injection ($p_{\text{attack}}=1.0$).