Multi-Mode Propulsion System

• Multi-mode propulsion systems are advanced architectures featuring multiple operational configurations tailored to diverse mission demands in environments like space, air, and water.
• They integrate varied energetic, kinematic, and physical reconfiguration methods, employing sophisticated control and optimization techniques to balance efficiency and thrust.
• Applications include spacecraft rendezvous, aerial‐aquatic vehicles, and planetary robotics, offering improved mission duration, payload delivery, and adaptability.

A multi-mode propulsion system is a propulsion architecture that provides two or more distinct operational modes, each tailored for different performance objectives, environments, or phases of a mission. In contemporary research and engineering, such systems are formulated to optimize the trade-off between efficiency and maneuverability by selecting, switching between, or blending multiple modes—discrete or hybridized—in real time or along precomputed trajectories. These systems are prominent in advanced spacecraft, aerial-aquatic vehicles, and planetary robotics, with operational modes often differing in thrust magnitude, specific impulse, actuation principle, or physical configuration.

1. Physical and Operational Definitions

A multi-mode propulsion system, in the context of aerospace engineering and robotics, encompasses any mechanism with at least two distinct operational configurations. These can be:

• Discrete propulsive regimes (e.g., low-thrust/high-Isp electric versus high-thrust/low-Isp chemical)
• Physical reconfiguration of actuators for different media (e.g., air vs. water)
• Adaptations in force transfer (e.g., vectoring, switching, or morphing of thrust direction/mechanism)

Key differentiators include the medium of operation (air, water, vacuum), propulsive physics (electrodynamic, chemical, mechanical), and discrete or continuous configurability with respect to mission phases.

For example, in dual-mode space propulsion, high-thrust chemical engines are combined with high-Isp electric thrusters, sharing a common propellant resource and engaged selectively to optimize either rapid maneuvering or cruise efficiency (III et al., 9 Sep 2025). In bioinspired aerial-aquatic vehicles, a single actuator architecture (e.g., flapping wing) reconfigures its kinematics to satisfy force demands for both flight and swimming (Izraelevitz et al., 2014).

2. Kinematic and Control Principles

The distinguishing property of such systems is the existence of mode-dependent kinematic and control laws. For illustrative purposes:

• Dual-Medium Flapping Mechanism: In (Izraelevitz et al., 2014), the wing kinematics are defined by three joint motions—inline sweep θ₁(t), heaving θ₂(t), and pitching θ₃(t)—with the effective force envelope determined by the stroke angle β:
  • Bird-like mode ($β < 90°$): Enhances lift via forward inline sweeping.
  • Turtle-like mode ($β > 90°$): Prioritizes thrust, suppresses vertical oscillations.
  • The kinematic relationships couple θ₁ and θ₂ via $A₁ = A₂ / \tan(-β)$ (Equation 2), dictating the amplitude envelope according to the selected mode.
• Multi-Engine, Multi-Mode Electric Propulsion: In high-fidelity trajectory optimization, each engine or engine cluster can operate at discrete power levels, and the control law is constructed by smooth blending of activation functions to approximate discrete switches, allowing for efficient numerical optimization. The general composite control is:

$$u_k = \sum_{i=1}^{N_{b,k}} \left( \prod_{j=1}^{N_{c,k,i}} \zeta_{i,j} \right) u_{b,i}$$

where $\zeta_{i,j}$ are smoothed activation functions governing the blending between modes (Taheri et al., 2019).

• Adaptive Direct Optimization: For systems using discrete mode switches (e.g., singular thrust/power pairs), the selection along the trajectory is posed as a smooth function of state and costate, enabling the system to autonomously transition between operational points based on mission constraints and system state (Saloglu et al., 28 Aug 2024, III et al., 9 Sep 2025).

3. Optimization Techniques and Computational Frameworks

Multi-mode propulsion systems inherently pose hybrid (continuous-discrete) optimal control problems. Notable methodologies to address these complexities:

• Composite Smooth Control (CSC): Instead of explicitly modeling switching times (which yield multi-point boundary value problems), CSC replaces the original discontinuous controls with analytically smooth surrogates, transforming the problem into a standard two-point boundary value problem amenable to indirect variational methods (Taheri et al., 2019, Taheri et al., 2019). As smoothing parameters approach zero, the solution approaches the discrete switching policy.
• Direct Optimization with Mode Smoothing: Utilizing homotopy/continuation-based smoothing, discrete mode selections are embedded into the optimization framework. For instance, (Saloglu et al., 28 Aug 2024) employs smoothed switching functions $S_k(u; ε)$ (where ε is a small parameter), ensuring the optimizer can traverse mode transitions without resorting to combinatorial search or suffering from gradient discontinuities.
• Adaptive Collocation Methods: Advanced direct collocation, such as Legendre–Gauss–Radau (LGR), is used for phase-partitioned multi-mode trajectory planning. This approach provides mesh refinement where control switches are expected, accurately capturing bang–bang and coasting arcs even under strong propellant constraints (III et al., 9 Sep 2025).

4. Applications Across Domains

The demand for multi-mode propulsion spans terrestrial, atmospheric, and space domains:

• Spacecraft Transfer and Rendezvous: Multi-mode architectures are used to optimally transfer between periodic orbits in complex gravitational environments. Low-thrust electric modes are employed for cruise/loiter, while high-thrust chemical modes enable rapid maneuvers. Integrated trajectory and system design demonstrates reduced mission duration and improved payload mass compared to single-mode schemes, particularly when high-thrust resources are severely limited (III et al., 9 Sep 2025, Saloglu et al., 28 Aug 2024).
• Aerial-Aquatic and Triphibian Vehicles: Systems such as morphable flapping wings (Izraelevitz et al., 2014) or reconfigurable ducted propellers (Yang et al., 2022) exploit multi-mode principles to enable seamless transition and efficient propulsion in air, water, and on land. Kinematic architectures are engineered to fundamentally alter the direction and magnitude of generated forces according to the requirements of each physical environment.
• Planetary Robotic Navigation: Multi-mode control schemes, driven by vision-LLMs, select among specialized navigation modes (efficient, safe, conservative) based on real-time hazard classification, balancing time and energy efficiency against safety for complex terrain traversal (Cheng et al., 20 Jun 2025).

5. Experimental Validation and Performance Metrics

Validation strategies for multi-mode systems span theory, simulation, and hardware:

• Force Envelope Characterization: Wind tunnel and towing tank validation for bioinspired mechanisms reveal that forward–inline (bird-like) operation achieves mean vertical force coefficients ($C_y$) up to 1.1, sufficient for supporting aerial vehicle weight, while backward–inline (turtle-like) operation yields thrust coefficients ($C_x$) ≈ 0.24 with suppressed vertical oscillations optimal for aquatic locomotion (Izraelevitz et al., 2014).
• Case Study: Earth-to-Comet Rendezvous: Direct co-optimization accommodates discrete mode selection and solar array sizing, increasing delivered payload and reducing required power system mass versus single-mode designs (Saloglu et al., 28 Aug 2024).
• Three-Body Dynamics Transfer: Multi-mode propulsion, when combined with propellant constraints, reduces overall transfer time versus single-mode solutions, especially as constraints become more stringent; this is quantitatively established in ER3BP periodic orbit transfers (III et al., 9 Sep 2025).
• Robotic Navigation Efficiency: Dynamic mode switching via VLMs in rover navigation enables up to 79.5% reduction in traversal time relative to single-mode conservative methods, without sacrificing safety (Cheng et al., 20 Jun 2025).

6. Challenges, Trade-offs, and Systematic Design

Design and optimization of multi-mode systems face several challenges:

• Non-smoothness and Discrete Transitions: Abrupt mode switches introduce Jacobian discontinuities, complicating convergence of classical optimization algorithms. Smoothing frameworks (e.g., CSC) alleviate this but require careful selection of regularization parameters and validation against the limit behavior.
• Propellant Constraints and Mode Schedulability: In shared-propellant architectures, optimal allocation of high-thrust resource under mass-limited scenarios necessitates precise phase partitioning and enforcement that at most one mode is active at any moment ($δ_1 \cdot δ_2 = 0$), as imposed through path constraints in the optimization (III et al., 9 Sep 2025).
• Physical Hardware and Environmental Adaptability: Realizing actuator kinematics that operate efficiently across media with orders-of-magnitude disparity in density and viscosity (e.g., air vs. water) demands innovative mechanisms (such as planetary gearboxes for torque-speed matching or morphable propeller mounts).
• Integration with System Design: The interplay between propulsion, power, and trajectory requires co-optimization. For example, solar array sizing must be optimized together with the propulsion mode schedule to avoid unnecessary mass overhead in electric propulsion spacecraft (Saloglu et al., 28 Aug 2024).

7. Systematic Frameworks and Future Implications

Recent methodological advances provide systematic frameworks for generalized multi-mode optimization:

• Unified problem formulations that partition the trajectory into phases (coast, transfer, coast), embed true anomaly as the independent variable to eliminate redundancy in time discretization, and enforce phase and path continuity. This enables rigorous extension to arbitrary multi-mode and multi-domain mission design in complex dynamical environments (III et al., 9 Sep 2025).
• The general applicability of the described frameworks suggests that emerging missions—requiring operation across heterogeneous environments or complex mission phases—will increasingly depend on multi-mode propulsion architectures rigorously optimized using smoothing and collocation-based direct methods.

---

In summary, multi-mode propulsion systems represent a class of mission-critical technologies that rely on dynamic or scheduled switching among a set of actuator modes—kinematic, energetic, or environmental—to deliver superior adaptability in demanding mission profiles. Their rigorous treatment in modern control and optimization frameworks, substantiated by empirical validation, is central to achieving efficient, robust, and physically feasible solutions in advanced aerospace and robotic applications.