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From Multi-Modal Paths to Executable Trajectories: A Trajectory Planning Framework for 4WIS Robots

Runjiao Bao, Lin Zhang, Yongkang Xu, Shoukun Wang

arXiv:2608.29108v1cs.RO

TL;DR

Global planning for 4WIS robots must coordinate motion-mode selection rather than defer it to execution, because switching can affect execution reliability. The paper combines mode-augmented Hybrid A* with mode-consistent segment-wise optimization, achieving safe, accurate, efficient trajectories and successful physical-robot execution.

  • Problem

    Existing 4WIS planning methods often defer motion-mode selection to execution, leaving global mode coordination insufficiently addressed and increasing execution uncertainty.

  • Method

    The framework extends Hybrid A* with explicit motion modes, switching-aware costs and heuristics, and multi-modal terminal connections, then optimizes fixed-mode trajectory segments with stationary transitions.

  • Results

    The proposed method generates safe trajectories with zero terminal pose error, shortest arrival and computation times among compared planners, and accurate physical-robot tracking.

  • Takeaways & Limitations

    The framework provides an executable solution for exploiting 4WIS maneuverability in constrained and structured environments.

Abstract

from arXiv · show

Four-wheel independent steering (4WIS) mobile robots support multiple motion modes, offering high maneuverability in narrow and complex environments. However, existing planning methods often fail to fully exploit these capabilities, leading to suboptimal trajectory quality. To address this limitation, this paper proposes a multi-modal global trajectory planning framework that couples mode-augmented front-end search with mode-consistent segment-wise trajectory optimization. In the front-end stage, Hybrid A* is extended to a four-dimensional state space incorporating motion modes, while mode-switching-aware cost and heuristic functions embed mode decisions into the global search process. Multi-modal Reeds-Shepp curves and an intelligent terminal connection strategy are further designed to improve search efficiency. In the back-end stage, a segment-wise trajectory optimization framework based on an improved iterative safe corridor scheme is developed to convert discrete multi-modal paths into smooth, kinematically feasible trajectories with stationary mode transitions. Experimental results show that the proposed method achieves the best overall performance in safety, arrival time, terminal accuracy and computation time. Real-world experiments on a physical 4WIS robot further validate the practical effectiveness and executability of the generated trajectories, providing a flexible and high-performance solution for multi-modal mobile robot trajectory planning.

I. INTRODUCTION

4WIS robots offer multiple motion modes for constrained environments, but global planning methods often defer mode selection to execution and inadequately coordinate switching. This section frames trajectory planning as finding collision-free, kinematically feasible motion in a bounded workspace.

  • 4WIS robots provide multiple motion modes, but global planning remains less explored than tracking control and kinematic modeling.
  • Deferred mode selection can increase execution uncertainty, while non-stationary switching may introduce transient instability and reduce reliability.
  • Most prior mode-switching approaches decide modes during execution from a predefined reference trajectory rather than modeling them during global planning.
  • A. Trajectory Planning Problem Statement: The planning problem seeks a feasible trajectory from an initial to a goal configuration within the collision-free configuration space.
  • A. Trajectory Planning Problem Statement: Valid paths must satisfy kinematic feasibility and collision avoidance, including steering and motion-continuity limits between adjacent waypoints.

B. 4WIS Robots Motion Modes

The 4WIS model represents three classical motion modes through an equivalent bicycle model and maps center velocity and steering variables to the physical wheels. Each mode imposes distinct geometric and directional motion characteristics.

  • The 4WIS system supports Ackermann steering, lateral steering, and parallel movement.
  • The equivalent bicycle model uses virtual-wheel steering and center velocity, then maps them to four-wheel steering angles and driving velocities.
  • The system state includes robot position, heading, signed center velocity, and equivalent steering angle, while acceleration and steering rate form the controls.
  • The discrete model applies a mode-specific body kinematic function while retaining an identical control-input matrix across motion modes.
  • Ackermann motion supports conventional driving and smooth turning, whereas lateral steering supports structured parking and lateral pose adjustment.
  • Parallel movement keeps the heading constant and aligns the robot-center velocity with the common wheel direction, supporting fixed-orientation avoidance and docking.

C. Collision Model

The collision model approximates the robot footprint with two circles and inflates obstacles by the circle radius plus a safety margin. Collision checking then tests the circle centers against the inflated obstacle region.

  • The robot footprint is approximated by two equal-radius circles placed along its longitudinal axis to cover the front and rear body regions.
  • The circle radius is defined geometrically for the footprint approximation and is used in subsequent obstacle inflation.
  • Obstacle inflation uses the Minkowski sum of obstacles with a disk of radius rc = rb + rsafe, reducing collision avoidance to checking both circle centers.
  • The safety margin is set to 0.02 m in all experiments, providing conservative footprint accounting during fast collision checks.

IV. METHODOLOGY

The framework combines mode-aware Hybrid A* search with motion-mode-specific primitives, terminal connections, and explicit switching operations. This front-end produces multi-modal paths while accounting for mode-dependent motion and switching behavior.

  • The framework integrates front-end path generation with back-end trajectory optimization to produce collision-free, kinematically feasible navigation.
  • Hybrid A* is selected because modular motion primitives, heuristics, and terminal connections facilitate integrating 4WIS multi-modal maneuverability.
  • When near the goal, Reeds–Shepp terminal connections return a solution immediately if collision-free; otherwise regular search expansions continue.
  • 1) Multi-Modal State Representation:: The state space is extended from (x, y, θ) to (x, y, θ, m), explicitly representing the current motion mode.
  • 1) Multi-Modal State Representation:: The three motion-mode labels correspond to Ackermann steering, lateral steering, and parallel movement, with parallel primitives holding heading constant.
  • 1) Multi-Modal State Representation:: Reference velocity and sampling time determine primitive distance dynamically as Δs = vref × Δt, keeping motion-primitive lengths consistent across modes.
  • 1) Multi-Modal State Representation:: Search expansion includes intra-mode primitives and inter-mode operations that change only the mode label while inserting a switching node at the current pose.
  • 1) Multi-Modal State Representation:: Parallel-mode expansion updates the common wheel angle through sampled steering increments, while Ackermann and lateral modes update heading using their yaw-rate models.

2) Multi-Modal Reeds-Shepp Curves:

The planner extends Reeds–Shepp curves with motion-mode-dependent curvature bounds and incorporates mode-switching costs into Hybrid A* search. A unified cost and heuristic lets feasible modes compete without separate rule-based pruning.

  • Mode-dependent curvature: Mode-dependent curvature bounds adapt Reeds–Shepp curves to Ackermann, lateral steering, and parallel translation modes.Ackermann and lateral steering use geometric limits, while parallel translation couples curvature to translational speed.
  • Mode-dependent curvature: Lateral steering reuses Reeds–Shepp construction through an equivalent coordinate transform that exchanges the effective forward axis and wheelbase.The resulting curve is mapped back to the original frame; parallel translation is activated only below a heading-error tolerance.
  • Switching-aware cost: A mode switch is modeled as velocity reconfiguration plus switching latency, with preset switching time and acceleration determining its cost.At the initial node, starting from rest halves the velocity-related term.
  • Switching-aware cost: The accumulated cost adds switching penalties through an indicator for changes between the current and previous motion modes.At mode-switching nodes, only the switching cost is retained and other incremental terms are set to zero.
  • Unified search evaluation: The heuristic combines Euclidean and mode-specific Reeds–Shepp estimates, preserving Hybrid A* admissibility while improving cost estimation.All feasible modes are evaluated with f(n) = g(n) + h(n), so lower-cost modes are prioritized without pruning alternatives.

4) Terminal Connection Strategy:

The terminal strategy evaluates collision-free multi-modal Reeds–Shepp connections and selects the minimum-cost one, while the back end constructs adaptive safe corridors around the resulting path. Direction-guided expansion and local refinement produce corridor constraints for continuous optimization.

  • Terminal connection strategy: Near the goal, candidate terminal connections include current-mode and alternative-mode Reeds–Shepp paths with their switching costs.The minimum-cost feasible connection is selected, preserving kinematic feasibility while improving connection efficiency through mode selection.
  • Safe-corridor construction: The back end constructs convex feasible regions around resampled reference paths to constrain continuous trajectory optimization.Front and rear circle-center paths are used to synchronously build local safety corridors.
  • Terminal connection strategy: The front-end search attempts sorted multi-modal Reeds–Shepp connections and returns the first collision-free path before continuing regular expansions.The algorithm separately generates intra-modal and inter-modal successors, then evaluates switching-aware costs and heuristics.
  • Safe-corridor construction: Motion-direction-guided expansion prioritizes corridor growth according to the local velocity direction instead of fixed orthogonal cycling.The workspace is divided into four directional areas, and the selected direction determines expansion priority.
  • Safe-corridor construction: Collision checking follows each expansion step; collisions reduce the step from ∆d1 to ∆d2, and expansion stops at repeated collision or dmax.The resulting corridors become linear box constraints after discretization over N uniform time steps.

2) Iterative Optimization Framework:

The back end divides the reference path at mode-switching points and optimizes each fixed-mode segment within iteratively reconstructed safe corridors. Shared switching poses are preserved and velocities are constrained to zero, while soft penalties and warm starts improve numerical robustness.

  • Segment-wise optimization: The discrete reference path is divided into S segments at front-end mode-switching points, with each segment optimized under fixed mode-specific kinematic constraints.Each segment uses a corresponding time interval Tr; the switching points remain boundary conditions.
  • Stationary transitions: Each adjacent segment shares the same geometric switching pose and enforces zero velocity, making every mode transition stationary.Position and orientation remain fixed at switching points while internal states and controls are optimized.
  • Stationary transitions: Optimized segments are concatenated with a mode-reconfiguration interval tswitch inserted at every switching point.This preserves pose consistency while accounting for stationary reconfiguration time.
  • Numerical optimization: Each fixed-mode segment is solved as an NLP initialized by temporal resampling and kinematic interpolation of the front-end path.The resulting feasible warm start improves convergence robustness, while selected constraints are relaxed through soft penalties.
  • Numerical optimization: The optimization penalizes kinematic and geometric infeasibility alongside completion time and comfort, terminating when infeasibility falls below εtol or the iteration limit is reached.Otherwise, a new safe corridor is reconstructed using the previous optimized variables.

A. Experimental Setup

The evaluation uses four representative 4WIS environments, repeated trials, common robot models, and metrics covering planning time, safety, trajectory quality, terminal accuracy, and motion standardness. Simulation runs use CasADi with IPOPT on specified CPU and GPU hardware.

  • Experimental setup: Experiments use a platform with an Intel i7-13700H CPU and NVIDIA RTX 4060 GPU, with CasADi and IPOPT solving the back-end NLP.The robot’s geometric, kinematic, and planning parameters are summarized in Table I.
  • Experimental setup: Four scenarios test narrow-corridor detouring, constrained terminal poses, lateral transfer, and dense-obstacle trajectory generation.The environments target global mode switching, terminal maneuverability, lateral-motion capability, and cluttered-space planning.
  • Experimental setup: Each scenario is repeated 50 times under identical robot models and experimental settings for statistical comparison.The resulting metrics assess planning efficiency and overall performance.
  • Evaluation metrics: The evaluation measures standard-mode rate, computation time, safety, trajectory length, arrival time, curvature, and terminal position and yaw errors.Safety requires collision-free execution, while arrival time measures duration to the terminal state.
  • Evaluation metrics: Terminal position error is the Euclidean distance to the desired goal position, while terminal yaw error is the absolute wrapped heading error.These metrics quantify final positional and heading accuracy separately.
  • Evaluation metrics: Standard-mode rate measures the proportion of samples matching predefined parallel, Ackermann, lateral Ackermann, in-place rotation, or stop templates.A lower SMR indicates more non-standard motions and greater control difficulty.

1) Compared Methods:

The comparison evaluates Multi-SC against a single-mode variant and two external baselines across four benchmark scenarios, combining trajectory visualizations, quantitative performance, and an ablation study. Multi-SC provides the strongest overall balance of safety, terminal accuracy, mode consistency, arrival time, and computational efficiency.

  • Compared Methods: Multi-SC performs mode-augmented global search followed by trajectory optimization in mode-consistent safe corridors, whereas Single-SC restricts front-end search to Ackermann steering.The external baselines are ICR, which smooths a general 4WIS path, and MPPI, which performs local sampling-based planning and control.
  • Overall Comparison: Multi-SC generates safe trajectories in all four scenarios with zero terminal position and yaw errors, SMR of 1.000, and the shortest arrival and computation times.SMR indicates conformity of the entire trajectory to predefined standard motion modes.
  • External Baselines: ICR produces short geometric trajectories in Env2–Env4 but is unsafe in all four environments because its back-end smoothing does not explicitly consider obstacle constraints.Its SMR ranges from 0.715 to 0.764, indicating substantial motion outside the predefined standard 4WIS modes.
  • External Baselines: MPPI is collision-free in every scenario but has the longest arrival time, substantially higher computation time, noticeable terminal errors, and SMR ranging from 0.720 to 0.904.The terminal errors are associated with the absence of an explicitly enforced exact terminal-state constraint.
  • Overall Comparison: 4.4%, 6.7%, and 30.6%: Multi-SC reduces trajectory length, arrival time, and computation time relative to Single-SC by these average amounts.The gains are attributed to selecting lateral or parallel motion when environmental structure makes Ackermann-only planning detour unnecessarily.
  • Ablation Study: In Env4 ablation, multi-modal primitives provide reachability, RS terminal connection removes terminal error, and switching regulation reduces unnecessary transitions and computation.Only MP has 0.202 m terminal position error; MP+RS has 18.745 m equivalent length and highest computation time; MP+SCH has 15.500 m equivalent length but 0.195 m terminal error; Full achieves zero terminal errors, shortest equivalent length, and lowest computation time.

2) Sensitivity to the Reference Velocity:

The reference velocity vref shapes motion-mode preferences by changing the relative switching cost, creating a trade-off between multi-modal flexibility and conservative mode consistency. Real-world experiments further show that the proposed framework produces faster, efficiently planned, and accurately tracked trajectories.

  • Reference-velocity sensitivity: Reference velocity changes the relative mode-switching cost in front-end search, leading to different motion-mode preferences.The planner was evaluated with three representative reference velocities in the same structured scenario.
  • Reference-velocity sensitivity: At vref = 1.0 m/s, low switching penalties encourage flexible combinations of Ackermann, lateral, and parallel motions.
  • Reference-velocity sensitivity: At vref = 1.5 m/s, unnecessary mode transitions are suppressed while the advantage of lateral motion is retained.
  • Reference-velocity sensitivity: At vref = 2.0 m/s, mode selection becomes more conservative, producing paths dominated by Ackermann motion.
  • Reference-velocity sensitivity: Smaller reference velocities favor frequent use of different modes, whereas larger values favor fewer transitions and stronger mode consistency.
  • Real-world validation: In real-world experiments, the multi-modal trajectory completed the task in 15.09 s versus 18.46 s for the single-modal trajectory.Front-end planning and back-end optimization took 0.82 s and 0.57 s, respectively, for a total pre-execution planning time of 1.39 s.
  • Real-world validation: Tracking errors remained low, with average and maximum lateral errors of 0.0096 m and 0.0388 m, and longitudinal errors of 0.0086 m and 0.0293 m.Tracking used an MPC controller at approximately 20 Hz after removing mode-switching intervals.
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